  In quantum field theory, an orbifold is a way to obtain a new theory from an
old one by gauging a finite global symmetry. This definition of orbifold does
not make sense for quantum gravity theories, that admit (conjecturally) no
global symmetries. In string theory, the orbifold procedure involves the
gauging of a global symmetry on the world-sheet theory describing the
fundamental string. Alternatively, it is a way to obtain a new string
background from an old one by quotienting some isometry. We propose a new
formulation of string orbifolds in terms of the group of gauge symmetries of a
given string model. In such a formulation, the `parent' and the `child'
theories correspond to different ways of breaking or gauging all potential
global symmetries of their common subsector. Through a couple of simple
examples, we describe how the higher group structure of the gauge group in the
parent theory plays a crucial role in determining the gauge group and the
twisted sector of the orbifold theory. We also discuss the dependence of this
orbifold procedure on the duality frame.
