Universal spaces for finite group actions on spaces of type $K(π,1)$

Abstract: In this paper author proposes a construction of a universal space of type $K(\pi,1)$ such that any action (up to homotopy conjugation) of a given finite group $G$ on spaces of the same homotopy type is presented on the constructed space. Moreover, any action of $G$ on any space of type $K(\pi,1)$ is covered by some action of $G$ on this universal space.