On Nielsen realization and manifold models for classifying spaces

We consider the problem of whether, for a given virtually torsionfree discrete group Γ Γ , there exists a cocompact proper topological Γ Γ -manifold, which is equivariantly homotopy equivalent to the classifying space for proper actions. This problem is related to Nielsen Realization. We will make the assumption that the expected manifold model has a zero-dimensional singular set. Then we solve the problem in the case, for instance, that Γ Γ contains a normal torsionfree subgroup π π such that π π is hyperbolic and π π is the fundamental group of an aspherical closed manifold of dimension greater or equal to five and Γ / π Γ /π is a finite cyclic group of odd order.