  In this paper we apply decomposition to orbifolds with quantum symmetries to
resolve anomalies. Briefly, it has been argued by e.g. Wang-Wen-Witten,
Tachikawa that an anomalous orbifold can sometimes be resolved by enlarging the
orbifold group so that the pullback of the anomaly to the larger group is
trivial. For this procedure to resolve the anomaly, one must specify a set of
phases in the larger orbifold, whose form is implicit in the extension
construction. There are multiple choices of consistent phases, which give rise
to physically distinct resolutions. We apply decomposition, and find that
theories with enlarged orbifold groups are equivalent to (disjoint unions of
copies of) orbifolds by nonanomalous subgroups of the original orbifold group.
In effect, decomposition implies that enlarging the orbifold group is
equivalent to making it smaller. We provide a general conjecture for such
descriptions, which we check in a number of examples.
