It was Ayn Rand who led to Wilson’s initial falling out with the company board. Around 2011, Wilson says, he clashed with Lululemon’s C.E.O. at the time, Christine Day, over his desire to feature quotations from “Atlas Shrugged” on a series of shopping bags. The book was so inspirational to Wilson that he wanted to share it with the Lululemon masses. “What I got out of it was: Make an incredible product, be true to yourself, be creative, treat your people really well and you can’t listen to naysayers,” he said. But after the first bag came out to a chorus of online derision, the company backed away from the plan. “The board totally rejected it: ‘We don’t want to offend anybody because brands aren’t supposed to offend anybody,’ ” Wilson recalled. He believed that Lululemon management wasn’t doing enough to spur innovation within the company. Frustrated with what he saw as the executives’ complacency, Wilson decided to go on a family sabbatical to Australia, a trip that laid the ground for a side project that may now threaten Lululemon itself.

During the year the Wilson family lived in Australia, Wilson’s wife, Shannon, who was a founding designer at Lululemon, began to work on a special new fabric she called “technical cashmere.” After Wilson was called back to Vancouver by the Lululemon board to help deal with the see-through Luon debacle, he and Shannon say they offered to give her new fabric to Lululemon free. This was the kind of innovation — casual wear with a luxurious feel — they felt the company needed. But management wasn’t interested. After Wilson’s apology video, they say, they offered the fabric again, this time at cost. Again, the Wilsons say, they were told no. (Lululemon would not comment.)

Wilson then engaged in a very public battle with the board about company governance. There was talk of a takeover, and then of a proxy fight. Wilson’s main concern, he told me, was that the company’s leaders seemed at that point to have “a total ignorance of competition.”

Wilson is no longer involved in Lululemon’s day-to-day operations, and last August, he sold half his Lululemon shares (more than 13 percent of the company) to Advent International, a private equity firm. In return, he says, he got “everything I wanted”: $845 million and a reconfiguration of the Lululemon board, which now has two new members from Advent who have completed Landmark training at Wilson’s request. Wilson has remained a board member and has promised not to wage a proxy fight for at least two years.

Shannon Wilson, meanwhile, left the company. With Wilson’s oldest son, J.J., she started a new line, Kit and Ace, selling $80 T-shirts and other apparel made of that “technical cashmere” fabric. The company describes itself as bridging the divide between “what you want and what you need.” Five stores have opened in Canada over the past seven months, and there are outposts in San Francisco and New York’s NoLIta. Its first shopping bags were printed with an essay about integrity by the Harvard Business School professor Michael C. Jensen.

Wilson said in January that the family has invested $7 million and expects to take on another $300 million in debt to finance the rollout, which includes plans for 95 more U.S. outlets by 2019. Wilson has insisted that he is nothing more than an adviser to Kit and Ace in order to retain his seat on the Lululemon board, but the two companies share an eerily similar ethos and strategy. Early on at Lululemon, Wilson came up with a “muse” who would inspire all merchandise — a 32-year-old professional single woman named Ocean who makes $100,000 a year. Wilson described Ocean to me like this: “engaged, has her own condo, is traveling, fashionable, has an hour and a half to work out a day.” Ocean was the target market, he explained, because she was the woman who all women want to be. “If you’re 20 years old or you’re graduating from university, you can’t wait to be that woman,” he said. “If you’re 42 years old with a couple children, you wish you had that time back.”

As Lululemon moved into men’s wear, the company added a male muse. Duke (who shared a name with Wilson’s third son) was 35 and made more money than Ocean. Duke was an “athletic opportunist,” surfing in the summer, snowboarding in the winter, and he was willing to pay for quality.