Given a smooth algebraic surface $X$, and a group $G$ acting on it and letting $Y := X / G$, how can we compute $K_Y^2$ from from $K_X^2$?
Current progress: In Borisov and Fatighenti - New explicit constructions of surfaces of general type, during the proof of theorem 2.2 this situation arises, and we have $K_X^2 = 42$, $K_Y^2 = 3$, and $G = C_{14}$, leading me to guess that there is some formula like $K_X^2 = \lvert G\rvert K_Y^2$. However, in some situations like Keum - Quotients of fake projective planes Theorem 1.1 (2), we have a surface with $K_X^2 = 9$ and $G = C_7$, so such a formula can't hold because the order of the group doesn't divide $K_X^2$.
Also, I'm looking for a "down-to-earth" (i.e. not full of étale jargon) reference for Galois quotients of varieties, especially the behavior of invariants like $K_Y^2$. I would even settle for a jargon-filled reference that shows how to precisely do computations.