Om Prakash Bhatt is intensely loyal to the State Bank of India (SBI). “This was a great bank, and it was seeing relatively bad days,” says Bhatt, who joined the bank in 1972 as a probationary officer and was named chairman in 2006. “They put me in the chairman’s seat, and it was up to me to do something. If not me, who would?” SBI—the country’s largest bank by assets—had fallen on tough times when Bhatt took charge of the state-owned institution. With roots stretching back to 1806, this stalwart of the Indian economy was losing market share to up-and-coming private banks and a growing list of foreign players reaching customers with new products and new technologies. State Bank, in which the government has a 60 percent interest, was languishing in inertia.

The prescription was innovation, but the challenge centered on getting 200,000 workers stretched across 10,000 branches to take their medicine. Communicating the need for change and shaking this huge corporate behemoth from its lethargy became the critical task ahead of Bhatt.

Bhatt, who spoke with McKinsey Quarterly editor Roger Malone in SBI’s corporate center, in downtown Mumbai, said it’s too early to be confident of success, although the...