With T. de Fernex, E. Lupercio, and B. Uribe.``A localization principle for orbifold theories,''

hep-th/0411037.

In this article, written primarily for physicists and (differential) geometers, we survey
several manifestations of a general localization principle for orbifold theories such as
$K$-theory, index theory, motivic integration, and elliptic genera.