Chern character in equivariant entire cyclic cohomology (Q1814102)

A \(G\)-quantum algebra is defined. It consists of a \(C^*\)-dynamical system \(({\mathcal A},G,p)\), with \(G\) finite, \(\mathbb{Z}_ 2\)-grading \(\gamma\) on \({\mathcal A}\), and superderivation \(d\) on Banach algebra \({\mathcal A}\). The Chern character in the equivariant entire cyclic cohomology is constructed. The character-valued index of the Dirac operator \(Q\) of a \(G\)-quantum algebra is expressed in terms of the Chern character and an equivariant \(K\)-theory class. This theorem generalizes \textit{A. Connes'} index theorem [\(K\)-theory 1, No. 6, 519-548 (1988; Zbl 0657.46049)].