2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/66950For an algebra B with an action of a Hopf algebra H we establish the pairing between even equivariant cyclic cohomology and equivariant K-theory for B. We then extend this formalism to compact quantum group actions and show that equivariant cyclic cohomology is a target space for the equivariant Chern character of equivariant summable Fredholm modules. We prove an analogue of Julg's theorem relating equivariant K-theory to ordinary K-theory of the C*-algebra crossed product, and characterize equivariant vector bundles on quantum homogeneous spaces.LaTeX2e, 16 pages; corrections plus a short discussion of K1K-Theory and HomologyOperator AlgebrasQuantum Algebratext