Symmetries, Quotients and Kaehler-Einstein metrics

We consider Fano manifolds M that admit a collection of finite automorphism groups G_1, …, G_k, such that the quotients M/G_i are smooth Fano manifolds possessing a Kaehler-Einstein metric. Under some numerical and smoothness assumptions on the ramification divisors, we prove that M admits a Kaehler-Einstein metric too.