  Inspired by work of Borzellino and Brunsden, we generalize the notion of a
submanifold identifying a natural and sufficiently general condition which
guarantees that a subset of an (effective) orbifold carries itself a canonical
induced orbifold structure. We illustrate the strength of this approach
generalizing typical constructions of submanifolds to the orbifold setting
using embeddings, proper group actions and the idea of transversality.
