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Zusammenfassung:
Recently it has been shown that D-branes in orientifolds are not always described by equivariant Real Ktheory. In this paper we define a previously unstudied twisted version of equivariant Real K-theory which gives the D-brane spectrum for such orientifolds. We find that equivariant Real K-theory can be twisted by elements of a generalised group cohomology. This cohomology classifies all orientifolds just as group cohomology classifies all orbifolds. As an example we consider the $Omega imesI_4$ orientifolds. We completely determine the equivariant orthogonal K-theory $KO_{Zop_2}(R^{p,q})$ and analyze the twisted versions. Agreement is found between K-theory and BCFT results for both integrally and torsion charged D-branes
