  In previous work the authors introduced a new class of modular quasi-Hopf
algebras $D^{\omega}(G, A)$ associated to a finite group $G$, a central
subgroup $A$, and a $3$-cocycle $\omega\in Z^3(G, C^x)$. In the present paper
we propose a description of the class of orbifold models of rational vertex
operator algebras whose module category is tensor equivalent to $D^{\omega}(G,
A)$-mod. The paper includes background on quasi-Hopf algebras and a discussion
of some relevant orbifolds.
