KIEV, Ukraine — During the Independence Square protests, Dmytro Yarosh made a name for himself as an expert with firebombs. Now, just weeks later, Mr. Yarosh, leader of the right-wing coalition known as Right Sector, says he is running for president.

When Russia’s politicized state media talk about the “neo-fascists” and “anti-Semites” who pulled off what the Kremlin calls a coup in Kiev and are now supposedly threatening Russians in Crimea and eastern Ukraine, they have men like Mr. Yarosh in mind.

But who these men really are and what they stand for, outside the caricatures in the Russian media’s fun-house mirror, are not always clear.

Other than his unstinting nationalism, penchant for secrecy and leadership role in the street fighting, little is publicly known of Mr. Yarosh, beyond that he is 42, a graduate of a teachers college and a man who has been active in Ukraine’s once-fringe right-wing politics for most of his life.