Abstract
For a bundle of compact Lie groups \(p\colon {\cal G} \to B\) over a compactum \(B\) (with the structure group of automorphisms of the corresponding group), we introduce the gauge-equivariant \(K\) -theory group \(K_{{\cal G}}^{0}(X; {\mathcal A} )\) of a bundle \(\pi_{X}\colon X \to B\) endowed with a continuous action of \({\cal G}\) constructed using bundles \(E\to X\) with the typical fiber being a projective finitely generated module over a unital \(C^*\) -algebra \( {\mathcal A} \) . The index of a family of gauge-invariant (= \({\cal G}\) -equivariant) Fredholm operators naturally takes values in these groups. We introduce and study products and use them to define the Thom homomorphism in gauge-equivariant \(K\) -theory and prove that this homomorphism is an isomorphism.
DOI 10.1134/S106192082460168X
