America is getting a new stock exchange from the most prominent critics of high-frequency trading.

After months of delays and a brutal lobbying battle that divided Wall Street, the IEX Group won approval on Friday from the Securities and Exchange Commission to become the nation’s 13th official stock exchange.

IEX is run by the people at the center of the Michael Lewis book, “Flash Boys: A Wall Street Revolt,” which profiles the early efforts of the IEX team to create a trading exchange that would be somewhat shielded from high-frequency traders.

Other exchanges and trading firms had urged the S.E.C. to reject the IEX application to become an exchange.

Opponents of IEX, including the other stock exchanges, have argued that the structure of the new exchange will add unnecessary new complexities into an already complex stock market, and potentially end up hurting small investors.