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.Comment: 21 pages LaTeX, one eps figur
