HELSINKI, Finland — Marc Dillon still remembers the sick feeling that overcame him when Nokia announced it was scrapping a software project that he and hundreds of other developers had spent years creating.

It was early 2011, and Nokia, the Finnish cellphone giant, was struggling to compete with the sudden rise of Apple and Samsung in the global smartphone market. In response, Nokia’s chief executive, Stephen Elop, ended the company’s plans for its own operating system and joined with Microsoft to focus on building Windows-based phones.

“I almost threw up when I heard the news,” said Mr. Dillon, an American engineer living in Finland, who was laid off after the company’s strategy shift. “Nokia did a lot of great things for a long time. We didn’t want to see this part of the story end.”

So Mr. Dillon and three other former Nokia executives took it upon themselves to prove their onetime bosses wrong.