  We consider smooth actions of totally disconnected groups on simplicial
complexes and compare different equivariant cohomology groups associated to
such actions. Our main result is that the bivariant equivariant cohomology
theory introduced by Baum and Schneider can be described using equivariant
periodic cyclic homology. This provides a new approach to the construction of
Baum and Schneider as well as a computation of equivariant periodic cyclic
homology for a natural class of examples. In addition we discuss the relation
between cosheaf homology and equivariant Bredon homology. Since the theory of
Baum and Schneider generalizes cosheaf homology we finally see that all these
approaches to equivariant cohomology for totally disconnected groups are
closely related.
