2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/77537We give a survey on the homotopy theory of the regular group of Banach algebras with emphasis on the unstable K-Theory of real and complex C*-algebrasK-Theory and HomologyOperator Algebras46L; 19K; 55Q52On the topology of the group of invertible elementstext