Recently Chen and Ruan inspired by ideas in String
Theory have discovered a remarkable new cohomology for orbifolds. Adem and Ruan have studied the corresponding K-theory. In this talk I survey my work with B. Uribe on this field. I explain how we can unify the twisted K-theory that Witten has put forward in String Theory with the Adem-Ruan theory by considering an orbifold as a stack and its twisting as a gerbe. I will also explain how Deligne Cohomology provides an elegant and unifying framework for several aspect of the theory, in partucular explaining the relation between the B-field and the discrete torsion in orbifold Type IIB supersting theories. Finally I will point out how this relates to the recent works of Freed, Hopkins and Teleman on twisted K-theories. |