One of the most feared men on Wall Street recently gave a tour of his offices with confident glee. From one window on the 44th floor, there is a view of the Statue of Liberty. On the other side is One World Trade Center.

Brad Katsuyama, 38, has the only enclosed office on the floor, but he rarely uses it. Dressed in jeans and wearing a fleece vest, he slides easily among his nearly 70 employees.

“This is where the action is,” he says, pointing to a desk in the middle of a crowded room.

From here, Katsuyama has drawn the attention of some of the biggest names on Wall Street with his four-year-old company, Investors’ Exchange, or IEX. The idea behind the company is simple: Provide a venue for investors who want to buy or sell stocks where sophisticated high-frequency traders, who can make thousands of trades in a blink of an eye, do not have the advantage.

The firm was the hero of Michael Lewis’s 2014 book “Flash Boys: A Wall Street Revolt,” which argued that the markets are rigged against mom-and-pop investors. Stock exchanges once dominated by screaming brokers, scrambling to get the best price on a stock, have been taken over by computers and traders using complex algorithms to find an advantage — measured in fractions of a second. High-frequency traders, Lewis argued, could always stay a step ahead.

In a keynote speech at the 2015 FinTech Startups Conference, IEX CEO and co-founder Brad Katsuyama explains how IEX solves a serious problem with Wall Street. (Empire Startups)

The book rankled many on Wall Street and thrust IEX into the spotlight.

Now, IEX could soon be competing against some of the oldest names on Wall Street, including the New York Stock Exchange, which is more than 200 years old. The Securities and Exchange Commission is expected to approve IEX’s application to become a registered stock exchange as early as Friday, a move that could shake up the institutions that have long dominated the way stocks are bought and sold.

IEX operates as a lightly regulated private one now, so investors cannot be forced to use it. That would change with approval, opening it up to a much larger market because traders have a duty to seek out the best price for their clients, be they pension funds or small investors.

“We have done everything we could possibly do. I feel content that we left it all on the field,” Katsuyama said.

IEX’s application has divided New York’s financial world and attracted high-profile detractors who say the start-up would add unnecessary complexity to the financial system and is asking for special treatment. IEX wants not only to slow down trades but also to process them in a potentially cheaper way, making it attractive to large pension funds or hedge funds that trade millions of shares of stock a day. Opponents worry that if the model catches on, it could be replicated across the industry.

Among its most strident opponents is Citadel, a massive hedge fund and securities dealer. “As the largest market maker, the efficient functioning of the market is incredibly important to us,” said Jamil Nazarali, head of ­execution services at Citadel Securities, the market making business of Citadel, which accounts for up to 15 percent of stocks traded on some days.

At the center of the debate is the value of 350 microseconds. (One microsecond is one millionth of a second. It is also about 1/1,000th of how long it takes to blink.)

That is how long IEX would delay every order to buy or sell a stock.

IEX says that what is known as its speed bump prevents high-speed traders from cutting the line to pick up stocks at the best prices, leaving slower mom-and-pop traders in the dust. Currently, a high-frequency trader can sniff out that the market is about to change directions and rush ahead of others using less-powerful computers. Slowing everyone’s trades helps create a level playing field, the company says.

But critics say the delay breaks a central covenant of the financial system: Exchanges should always show the best price available for a stock. Any delay, even a microscopic one, could wreak havoc, they say.

“A lot can happen in those 350 microseconds,” Nazarali said.

The debate is just the latest signal that the U.S. financial markets are evolving faster than regular investors, and many regulators, can keep up with. Instead of calling up a broker to buy 100 shares of stock, investors can now make the same trade — at a fraction of the cost — through a smartphone app. Many stocks are traded not by instinct or a careful study of the issues but by computers looking for technical advantages that will help them rack up profits pennies at a time. High-frequency traders were once on the fringe of the industry but now account for half of the stocks bought and sold a day.

And the key for most traders now is speed. The NYSE and Nasdaq composite index, at a price, offer access to key information fractions of seconds ahead of the rest of the market, a tremendously important advantage for high-frequency traders, who are so focused on speed that some put their computer servers in buildings near exchanges in hopes of gaining minuscule advantages in transmission times.

“If you [currently] pay big money to get ahead of everyone else, this could disrupt everything,” said David Becher, associate professor of finance at the Drexel University LeBow College of Business.

The evolution of the industry is also evident in where investors can make trades. Not long ago, there were few places to buy or sell stock, including the NYSE and Nasdaq. Now there are 12. IEX wants to become No. 13.

Katsuyama helped start IEX in 2012 after spending about a decade at the Royal Bank of Canada. It was there, he says, that he noticed the impact that high-frequency traders were having on the market. After the start-up was profiled by Lewis in “Flash Boys,” IEX grew quickly as a lightly regulated private exchange and gained some high-profile supporters.

Netscape co-founder James H. Clark and casino billionaire Steve Wynn are backers of the firm. (Clark is also on the company’s board.) It has also raised money from well-known hedge funds, including Pershing Square and Third Point Partners.

“The book, it was the best thing that could have ever happened to a company trying to do what we’re trying to do,” Katsuyama said.

Three years later, IEX is profitable but has less than 2 percent of the market. To compete on a large scale, the firm must move from its current configuration as a “dark pool” — a private exchange — to a regulated one. Currently, investors can choose whether to place a trade through IEX.

Vocal opposition, however, has slowed the regulatory process around its application. “Allowing IEX to become an exchange would create additional complexity in a marketplace that is already criticized — rightly — as too complex,” said Bill Harts, president of Modern Markets Initiative, which represents high-frequency traders.

The NYSE has launched repeated broadsides against the firm. “Like the ‘non-fat yogurt’ shop on Seinfeld, which actually serves tastier, full-fat yogurt to increase its sales, IEX advertises that it is ‘A Fair, Simple, Transparent Market,’ whereas it proposes rules that would make IEX an unfair, complex, and opaque exchange,” the NYSE, known as the Big Board, said in a filing to the SEC.

Lawyers for Nasdaq, the country’s largest exchange, have raised the prospect of a legal challenge if IEX’s application is approved. “The proposed interpretation would be unlikely to survive judicial scrutiny,” attorneys at Gibson, Dunn & Crutcher said in a letter to the SEC last month.

IEX is fine as a dark pool, critics say, but it should not be allowed to employ a speed bump as a regulated exchange.

“IEX is seeking exchange status, but they are requesting exemptions to the existing SEC rules that were designed to protect investors and promote more displayed orders,” Stacey Cunningham, chief operating officer of the NYSE, said in a statement.

But for market stalwarts, another threat could be on the horizon. Silicon Valley entrepreneur Eric Ries has started early talks to create an exchange, too. The Long-Term Stock Exchange “will seek to encourage long-term thinking through listing standards, guidance, tools, and services,” Ries said in his blog Monday.