  We investigate gauge anomalies in the context of orbifold conformal field
theories. Such anomalies manifest as failures of modular invariance in the
constituents of the orbifold partition function. We review how this
irregularity is classified by cohomology and how extending the orbifold group
can remove it. Working with such extensions requires an understanding of the
consistent ways in which extending groups can act on the twisted states of the
original symmetry, which leads us to a discrete-torsion like choice that exists
in orbifolds with trivially-acting subgroups. We review a general method for
constructing such extensions and investigate its application to orbifolds.
Through numerous explicit examples we test the conjecture that consistent
extensions should be equivalent to (in general multiple copies of) orbifolds by
non-anomalous subgroups.
