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.