Keith Laumer 
Worlds of the Imperium 

For Brion Bayard, the discovery of an alternate world to Earth where history took a different turn in the road was not a pleasant experience. His kidnapping brought him some startling revelations. Here was a world in which appeared identical doubles of famous personages—including a dangerous and hated dictator named Brion Bayard!

His assignment seemed simple enough. Dressed as his double, Brion was to enter the enemy stronghold, kill the dictator, and take his place until law and order could be maintained.

But once having seen his mirror-image brother, Brion had as little inclination to murder him as some other people had to let him live.