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There is the problem, whether for a given virtually torsionfree discretegroup $\Gamma$ there exists a cocompact proper topological $\Gamma$-manifold,which is equivariantly homotopy equivalent to the classifying space for properactions. 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 properactions, 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 aboutBrown's problem under certain conditions concerning the underlying group, forinstance if it is hyperbolic. In a sequel paper together with James Davis wewill deal with this  on the level of topological manifolds.

On Brown's Problem, Poincare' models for the classifying spaces for proper actions and Nielsen Realization