  We present the general form of the operators that lift the group action on
the twisted sectors of a bosonic string on an orbifold ${\cal M}/G$, in the
presence of a Kalb-Ramond field strength $H$. These operators turn out to
generate the quasi-quantum group $D_{\omega}[G]$, introduced in the context of
orbifold conformal field theory by R. Dijkgraaf, V. Pasquier and P. Roche. The
3-cocycle $\omega$ entering in the definition of $D_{\omega}[G]$ is related to
$H$ by a series of cohomological equations in a tricomplex combining de Rham,
Cech and group coboundaries. We construct magnetic amplitudes for the twisted
sectors and show that $\omega=1$ arises as a consistency condition for the
orbifold theory. Finally, we recover discrete torsion as an ambiguity in the
lift of the group action to twisted sectors, in accordance with previous
results presented by E. Sharpe.
