  The purpose of the article is to explain a new method to establish the
existence of an exceptional collection of length three for a fake projective
plane M with non-trivial automorphism group, related to a conjecture of
Galkin-Katzarkov-Mellit-Shinder in 2015. Our method shows that 30 fake
projective planes support such a sequence, most of which are new. In
particular, this provides many new H-phantom categories.
