Equivariant Differential Characters

We begin by wondering how one could classify topological (WZW) terms for a gauged sigma model.  This leads us to study the differential Borel quotient of a manifold with group action, which we use to define a notion of differential equivariant cohomology. 

Equivariant Chern-Weil theory naturally appears, and we answer a precise version of the original question.  A common theme will be the importance of connections in the differential Borel quotient.