You can measure the scale of Rebekka Bay’s job by the mighty view from her desk. We are on the 11th floor of the Gap headquarters in Tribeca, New York, where, as creative director, she commands her empire from a glass-walled corner office. Supersized marble meeting table; shelfie-ready stacks of art reference books; a Frank Stella print in the waiting area outside. And a view to the south-west, over the Hudson river, that is so beautiful at sunset that “between five and six o’clock, I don’t do any work. I just stare at the light.”

Sunset downtime notwithstanding, Bay, 44, has her work cut out. Her pedigree as the creator of H&M’s upscale, minimalist offshoot label Cos won her the Gap job, which she took on two years ago. It was a huge jump in scale, and profile. Cos is sold in 90 stores; Gap is sold in 1,700 stores worldwide, its performance under the spotlight of business pages globally. The size of the business means long lead times, so that the first collection overseen by Bay hit stores only this spring; this month sees the launch of the autumn collection, the first for which Bay has had her full team in place.

Gap is a huge ship to steer, and one that has lost its way. The darling of the American high street in the 90s and early noughties has been steadily losing ground for a decade. Once the go-to brand for contemporary basics, it has been assailed by a pincer-attack of industry game-changers: fast-fashion brands such as Zara have stoked an appetite for never-ending newness, while value labels such as Uniqlo offer the clean-cut jeans, padded jackets and T-shirts that were once Gap’s bread and butter, only with a lower price tag. The challenge of turning Gap around defeated Patrick Robinson, a designer who already had Armani, Perry Ellis and Paco Rabanne on his CV when he was hired with great fanfare in 2007 – and then let go in 2011.

Bay got the Gap job thanks to creating the upscale, minimalist H&M offshoot label Cos. Her collections include this, for spring/summer 2008. Photograph: Rex

At 8.30am, the door to Bay’s office is already open; I can see her bent over her BlackBerry, typing furiously. I knock and she stands to greet me with a smile and a handshake, and pulls two chairs together, so we can sit close. She is warm, has a slight Danish accent and is unselfconsciously attractive in that sunny, non-coquettish, Scandi-blond way. There is no grandiosity, no affectation. Bay is wearing a collarless, tunic-styled white shirt (Gap) and ankle-skimming jeans in washed-out black (Gap), with black Birkenstock sandals. In almost every photograph I have seen of her, she is wearing a white shirt and dark jeans or trousers. “A white shirt is kind of my uniform, because it always feels right,” she says. “I have friends who ask how it can be possible that I work in fashion, when I’ve worn the same thing for 25 years. I try to explain about nuances.” She laughs. I try, and fail, to imagine Karl Lagerfeld’s mates teasing him about what he wears to work.

What makes Bay’s job so tough is that while Gap is omnipresent – is there anyone reading this who doesn’t have a piece of Gap in their wardrobe? – in a way she doesn’t work in fashion at all. Mickey Drexler, the legendary CEO of Gap in its most profitable years, preferred to compare it to grocery shopping. In a Fortune magazine cover story in 1998, Drexler put it like this: “If you go into a supermarket, you would expect to find some fundamental items. You would expect to find milk: non-fat, 1%, 2%, whole milk. You’d expect the dates to be fresh. You want butter. You want certain types of bread. You have your list. I don’t know why apparel stores should be any different.” A Gap T-shirt is meant to be as fundamental a buy as a box of Kellogg’s cereal or a bar of Cadbury’s Dairy Milk.

Here, Bay says, her outsider status works to Gap’s advantage. “You need to be a foreigner to see the glamour in Campbell’s soup and Oreos. I really feel that excitement, and I want to celebrate that Americanness. My vision comes from my emotional Gap archive, which is about an American uniform: five-pocket jeans, khakis, T-shirts.”

The Gap take is an antidote to the aspirational-preppy, Ralph Lauren Wasp vision, more rooted in an idea of Americana that is sentimental, but democratic: road trips, watching games from the bleachers, coffee refills at the diner counter. On the window ledge in Bay’s office, just below the view, I notice a sumptuous coffee-table tome entitled Rock The Shack: The Architecture Of Cabins, Cocoons And Hide-outs.

This democratic vision is what made Gap fly. Think of the Khakis campaign, which featured casual portraits of American icons – Ernest Hemingway, Muhammad Ali – wearing khakis. Recently, Bay has been looking at Irving Penn’s Small Trades series of portraits of 1950s craftsmen and women in their working clothes – a cobbler in his heavy apron, a seamstress with her spectacles and pockets – in which the utilitarian garb of the sitters contrasts with the classical dignity of the photographs. The fabrics are rough and simple and worn, but their character is lovingly captured. There is little colour in the pictures, and “there is something about the way black washes in different fabrications that is really interesting”, Bay says. On the shop floor, this inspiration will translate into “black washes, but not stark black – an assortment from the darkest, inkiest black to a black so washed out that it’s a pale, pastelly grey. It’s a romantic take on something quite grungy.”

Facebook Twitter Pinterest Rebekka Bay: ‘Gap should be democratic inside as well as out.’ Photograph: Chris Buck/Guardian

Romance and emotion are words to which Bay returns again and again. “Gap is democratic, but it is aspirational as well. The idea that a simple T-shirt can be something more, the idea that you can wear a man’s simple shirt and look so sexy, that the product allows you to shine through. We need to deliver on that promise in everything we do. So it’s just a T-shirt, but there’s something in the drape of the neckline that makes it a little bit more. I always tell myself: if I put this T-shirt on a girl, I should want to be her.” In this sense, Bay reminds me a little of Jenna Lyons, the creative director of the more upscale American high-street name J Crew. Bay is softer, more easy-going, but they share a slightly geeky, straight-talking sense of what a garment stands for.

As well as emotion and glamour, a fashion brand needs constant newness. The customer who automatically drops a box of Coco Pops into her trolley each week, or picks up a bar of Dairy Milk as a petrol-station treat, has no such loyalty when it comes to buying clothes. “Being relevant is super-important to me,” Bay says. “I’m not trying to replicate high fashion or the catwalk, but Gap needs to be as relevant as Saint Laurent, just with a different customer target. And it is right that there should be some kind of connection between what we are doing and what Hedi Slimane is doing at Saint Laurent, because we are all tapping into the same collective mindset.”

Before Cos, Bay worked in trend forecasting. “I really believe in the concept of a collective mind, and how we gravitate towards something. Tapping into that is about picking up on how everyone is concerned with travelling. Or with local. Or with ecology. Those are the big ideas that we need to pick up on. Somehow you have to take that mood and describe it in a colouration, or a shape. Take this season. I think this is an anxious time, an uncertain time, there’s a lot of conflict in the world, so we gravitate towards something that’s close to home and romanticise that. I started with Kurt Cobain and Courtney Love, because there was something about them that felt very raw and real, and yet very romantic. And very American. And I translated that into all washed black denim, and soft rose-pinkish colours, and babydoll dresses.”

As a child in Silkeborg, Denmark, Bay “didn’t want to do fashion at all. As a kid, I always wanted everything in advance of everyone else. I wanted a camel sweater the year before everyone else wanted a camel sweater, which meant I never ever looked fashionable, because I was a little bit early on everything. For a while I wanted to be an architect. I wanted to communicate, to describe an emotion, and I wanted to do that visually. And in the end, well, clothes are faster than buildings. I am not sure I have the patience to be an architect.”

As part of her application for fashion school, she designed a collection to fit in a suitcase for a trip to America. “It was kind of a grunge collection, with floral dresses and big cardigans and biker boots. But I wrote in my assignment that I had left a space for a pair of jeans, because I would buy those when I got to America.” At college, Bay felt at odds with her surroundings. “This was in the era of the Antwerp Six, of Comme des Garçons, and fashion schools were very purist, all about artistic expression and design. I wanted to talk about how fashion was influenced by culture, so I was a little out of my time there.” After graduation, Bay spent eight years in London, working as a trend forecaster for Volvo, Nissan and Dunhill.

‘A romantic take on something quite grungy’: Gap’s autumn collection is the first for which Bay has had her full team in place. Photograph: Gap

A grounding outside the fashion bubble has given Bay a clear-eyed realism that should serve her well. “The second biggest change, moving to Gap, was shifting from Europe to America – that was a huge shift – but the biggest challenge of all is the scale of this company: how much you have to dial up to communicate. At Cos my voice could be quite intimate, but that won’t work here. If I want to do pretty, I can’t hint at pretty, I have to exaggerate pretty. I have to do floral on a babydoll dress and there have to be lots of them on the shop floor.” Internally, she is learning to speak louder. “I talk a lot. I try to create very clear frameworks, guardrails, product matrixes. And to make those very clear, because you can’t expect anyone to deliver unless you really explain to them exactly what it is they need to do. I spend very little time on my own at work. I wish I had more time alone, because it does get exhausting, but the only way to get everyone engaged in what you are doing is to have lots of open dialogue. Often, we have meetings of 20 people, and maybe just three or four people in that room could make those decisions, but by having more junior people in the room, you deepen their understanding. And Gap should be democratic inside as well as out, so it’s good to hear lots of opinions.” Famously, Bay kicked off one of her first design meetings by announcing, “Anyone who doesn’t have an opinion can leave the room now.” (“I’m Danish,” she laughs, and shrugs.)

One of Bay’s formative Gap memories comes from 2006, when she was living in London. It was the Christmas when Gap sold the multicoloured “Crazy Stripe” sweater, and everyone wanted one. “I wanted to wear it, I wanted to buy it for my sister and my mother. I went to every store in London, and it was sold out everywhere. I nearly got on a train to Manchester because a sales assistant on Oxford Street told me they still had some there. It was a happy stripe that made you smile, but it was also super-chic, super-tasteful.”

She never got that train to Manchester, but this winter the Crazy Stripe will be back in store, in a subtly updated form. “I’ve put it in my first winter collection, so that I have a chance to buy it. And because I really believe in that stripe. It’s got spirit.”

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