2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/163855A version of smooth K-theory is constructed, which is adapted to the total Chern class instead of the Chern character (contrarily to previous theories). Some total Chern class morphism from this K-theory to Cheeger-Simons differential characters is constructed. This answers a question raised by U. Bunke.Institution, keywords and AMS-classification codes addedDifferential GeometryK-Theory and Homology14F05; 19E20; 57R20text