For G a finite group, we develop some theory of G-equivariant piecewise-linear topology and prove characterization theorems for G-equivariant regular neighborhoods. We use these results to prove a conjecture of Csorba that the Lovász complex Hom(C5,Kn) of graph multimorphisms from the 5-cycle C5 to the complete graph Kn is equivariantly homeomorphic to the Stiefel manifold, Vn-1,2, the space of (ordered) orthonormal 2-frames in Rn-1 with respect to an action of the cyclic group of order 2.