Free properly discontinuous actions on homotopy surfaces

A homotopy surface is a finite-dimensional CW-complex having the homotopy type of a surface. We study free cellular actions of discrete groups on homotopy surfaces. For every such action of a finite group, we show that there is an action on a surface of the same homotopy type. We show that torsionfree groups of infinite cohomological dimension have no such actions on most homotopy surfaces. We classify the groups that act freely properly discontinuously on M2×R, where M2 is the closed orientable surface of genus 2.