2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/77258We expose a K-theoretic approach to study group C*-algebras and C*-algebraic compact quantum groups: 1. The conception of multidimensional geometric quantization and the index of group C*-algebras; 2. the entire homology of noncommutative de Rham currents and the noncommutative Chern characters, and their computation for C*-algebras of compact Lie groups and compact quantum groups.19 pages, AmSLaTeX2e fileK-Theory and HomologyDifferential GeometryOperator AlgebrasQuantum AlgebraRepresentation Theorytext