2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/66481The use of bundle gerbes and bundle gerbe modules is considered as a replacement for the usual theory of Clifford modules on manifolds that fail to be spin. It is shown that both sides of the Atiyah-Singer index formula for coupled Dirac operators can be given natural interpretations using this language and that the resulting formula is still an identity.10 pages, LaTeX (Added eference to preprint math.DG/0302050 by T. Aristide)Differential Geometry58J20text