D-branes on orbifolds with and without discrete torsion are analysed in a u
nified way using the boundary state formalism. For the example of the Z(2)
x Z(2) orbifold it is found that both the theory with and without discrete
torsion possess D-branes whose world-volume carries conventional and projec
tive representations of the orbifold group. The resulting D-brane spectrum
is shown to be consistent with T-duality.