2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/79343We present a K-theoritic approach to the Guillemin-Sternberg conjecture, about the commutativity of geometric quantization and symplectic reduction, which was proved by Meinrenken and Tian-Zhang. Besides providing a new proof of this conjecture for the full non-abelian group action case, our methods lead to a generalisation for compact Lie group actions on manifolds that are not symplectic. Instead, these manifolds carry an invariant almost complex structure and an abstract moment map.revised version, 55 pagesDifferential GeometryK-Theory and HomologySymplectic Geometrytext