Notes on discrete torsion in orientifolds

In this paper we discuss discrete torsion in orientifolds. In particular, we apply the physical understanding of discrete torsion worked out several years ago, as group actions on B$B$ fields, to the case of orientifolds, and recover some old results of Braun and Stefanski concerning group cohomology and twisted equivariant K theory. We also derive new results including phase factors for nonorientable worldsheets and analogues for C$C$ fields.