  The consistency of the orbifold action on open strings between D-branes in
orbifold theories with and without discrete torsion is analysed carefully. For
the example of the C^3/Z_2 x Z_2 theory, it is found that the consistency of
the orbifold action requires that the D-brane spectrum contains branes that
give rise to a conventional representation of the orbifold group as well as
branes for which the representation is projective. It is also shown how the
results generalise to the orbifolds C^3/Z_N x Z_N for which a number of novel
features arise. In particular, the N>2 theories with minimal discrete torsion
have non-BPS branes charged under twisted R-R potentials that couple to none of
the (known) BPS branes.
