Bloch's conjecture on certain surfaces of general type with $p_g=0$ and with an involution: the Enriques case

Abstract: In this short note we prove that an involution on certain examples of surfaces of general type with $p_g=0$, acts as identity on the Chow group of zero cycles of the relevant surface. In particular we consider examples of such surfaces when the quotient is an Enriques surface and show that the Bloch's conjecture holds for such surfaces.