2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/170022In this paper, we develop differential twisted K-theory and define a twisted Chern character on twisted K-theory which depends on a choice of connection and curving on the twisting gerbe. We also establish the general Riemann-Roch theorem in twisted K-theory and find some applications in the study of twisted K-theory of compact simple Lie groups.32 page. Thoroughly revised to improve the expositionK-Theory and HomologyDifferential Geometry55R65, 53C29text