  We find the orbifold analog of the topological relation recently found by
Freed and Witten which restricts the allowed D-brane configurations of Type II
vacua with a topologically non-trivial flat $B$-field. The result relies in
Douglas proposal -- which we derive from worldsheet consistency conditions --
of embedding projective representations on open string Chan-Paton factors when
considering orbifolds with discrete torsion. The orbifold action on open
strings gives a natural definition of the algebraic K-theory group -- using
twisted cross products -- responsible for measuring Ramond-Ramond charges in
orbifolds with discrete torsion. We show that the correspondence between
fractional branes and Ramond-Ramond fields follows in an interesting fashion
from the way that discrete torsion is implemented on open and closed strings.
