D-branes in Nonabelian Orbifolds with Discrete Torsion

We study IIB string theory on the orbifold R^8/Gamma with discrete torsion where Gamma is an arbitrary subgroup of U(4). We extend some previously known identities for discrete torsion in abelian groups to nonabelian groups. We construct explicit formulas for a large class of fractional D-brane states and prove that the physical states are classified by projective representations of the orbifold group as predicted originally by Douglas. The boundary states are found to be linear combinations of Ishibashi states with the coefficients being characters of the projective representations.