  There is the problem, whether for a given virtually torsionfree discrete
group $\Gamma$ there exists a cocompact proper topological $\Gamma$-manifold,
which is equivariantly homotopy equivalent to the classifying space for proper
actions. It is related to Nielsen's Realization and to the problem of Brown,
whether there is a d-dimensional model for the classifying space for proper
actions, if the underlying group has virtually cohomological dimension d.
Assuming that the expected manifold model has a zero-dimensional singular set,
we solve the problem in the Poincar\'e category and obtain new results about
Brown's problem under certain conditions concerning the underlying group, for
instance if it is hyperbolic. In a sequel paper together with James Davis we
will deal with this
  on the level of topological manifolds.
