Let $M$ be a manifold. Let a finite group $G$ act on $M$ discretely. Let $F$ be a field.
Suppose the induced action of $G$ on the cohomology algebra $H^*(M,F)$ is known. We want to obtain $H^*(M/G;F)$. Is there any method or procedure to follow? Can I quotient the action directly $H^*(M/G;F)=H^*(M;F)/G$?