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The purpose of this 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 nontrivial automorphism group, related to a conjecture of Galkin–Katzarkov–Mellit–Shinder in 2015. Our method shows that thirty fake projective planes support such a sequence, most of which are new. In particular, this provides many new $H$-phantom categories.

Exceptional Collection of Objects on Some Fake Projective Planes