We consider the problem of whether, for a given virtually torsionfree discrete group
Γ
\Gamma
, there exists a cocompact proper topological
Γ
\Gamma
-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
\Gamma
contains a normal torsionfree subgroup
π
\pi
such that
π
\pi
is hyperbolic and
π
\pi
is the fundamental group of an aspherical closed manifold of dimension greater or equal to five and
Γ
/
π
\Gamma /\pi
is a finite cyclic group of odd order.