Motivated by string theory on the orbifold ${cal M}/G$ in presence of a Kalb-Ramond field strength $H$, we define the operators that lift the group action to the twisted sectors. These operators turn out to generate the quasi-quantum group $D_{omega}
[G]$, introduced in the context of conformal field theory by R. Dijkgraaf, V. Pasquier and P. Roche, with $omega$ a 3-cocycle determined by a series of cohomological equations in a tricomplex combining de Rham, u{C}ech and group cohomologies. We further illustrate some properties of the quasi-quantum group from a string theoretical point of view.
