2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/75538In 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.29 pages, LaTeX2e, amsart, xyK-Theory and HomologyOperator Algebras46L80text