2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/78312We prove the index theorem for elliptic operators acting on sections of bundles where fiber is equal to a projective module over a C*-algebra, in the situation of action of a compact Lie group on this algebra as well as on the total space commuting with symbol. As an application the equivariant index theorem for families over the direct product of base by the space of parameters is obtained.LaTeX 2.09 + xypic, 51 pages, preprint is a detailed version of a combination of two papers to appear in "J. Math. Sci." and "Ann. Global Anal. Geom."Operator AlgebrasDifferential GeometryK-Theory and HomologyRepresentation Theory19Kxx, 46Lxx (Primary) 19K56, 19K35, 35S05, 47G30, 57R99, 57Sxx, 58G12 (Secondary)text