  In a previous paper we have introduced the gauge-equivariant K-theory group
of a bundle endowed with a continuous action of a bundle of compact Lie groups.
These groups are the natural range for the analytic index of a family of
gauge-invariant elliptic operators (i.e. a family of elliptic operators
invariant with respect to the action of a bundle of compact groups). In this
paper, we continue our study of gauge-equivariant K-theory. In particular, we
introduce and study products, which helps us establish the Thom isomorphism in
gauge-equivariant K-theory. Then we construct push-forward maps and define the
topological index of a gauge-invariant family.
