2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/167111A Frechet algebra endowed with a multiplicatively convex topology has two types of invariants: homotopy invariants (topological K-theory and periodic cyclic homology) and secondary invariants (multiplicative K-theory and the non-periodic versions of cyclic homology). The aim of this paper is to establish a Riemann-Roch-Grothendieck theorem relating direct images for homotopy and secondary invariants of Frechet m-algebras under finitely summable quasihomomorphisms.80 pages. v1: This is essentially the first part of the preprint arXiv:0706.1937, with improvements. v2: minor corrections, almost the published versionK-Theory and Homologytext