  Following Hopkins and Singer, we give a definition for the differential
equivariant K-theory of a smooth manifold acted upon by a finite group. The
ring structure for differential equivariant K-theory is developed explicitly.
We also construct a pushforward map which parallels the topological pushforward
in equivariant K-theory. An analytic formula for the pushforward to the
differential equivariant K-theory of a point is conjectured, and proved in the
boundary case, in the case of a free action, and for ordinary differential
K-theory in general. The latter proof is due to K. Klonoff.
