See:
Cypher, the Fallen Angel; the Badab War (sub-categories: the Lamenters, the Mantis Warriors, the Executioners).
Cypher is quite possibly loyal, despite the fact that he's pretty much the most hunted man in the galaxy, by the Dark Angels and their successors (even if only the uppermost ranks know what's really going on).
During the Badab War, the named chapters renounced the rule of the Emperor - but then after Lufgt Huron fell, they tried to be accepted back into the Imperial fold. They were subjected to a 100 year crusade of penance, which is on the verge of being finished in the modern 40k universe.