  In this note we observe that, contrary to the usual lore, string orbifolds do
not describe strings on quotient spaces, but rather seem to describe strings on
objects called quotient stacks, a result that follows from simply unraveling
definitions, and is further justified by a number of results. Quotient stacks
are very closely related to quotient spaces; for example, when the orbifold
group acts freely, the quotient space and the quotient stack are homeomorphic.
We explain how sigma models on quotient stacks naturally have twisted sectors,
and why a sigma model on a quotient stack would be a nonsingular CFT even when
the associated quotient space is singular. We also show how to understand twist
fields in this language, and outline the derivation of the orbifold Euler
characteristic purely in terms of stacks. We also outline why there is a sense
in which one naturally finds B nonzero on exceptional divisors of resolutions.
These insights are not limited to merely understanding existing string
orbifolds: we also point out how this technology enables us to understand
orbifolds in M-theory, as well as how this means that string orbifolds provide
the first example of an entirely new class of string compactifications. As
quotient stacks are not a staple of the physics literature, we include a
lengthy tutorial on quotient stacks.
