Foliated models for orbifolds and their applications

A foliated model is constructed for every orbifold. Such model is a foliation with the leaf space coinciding with the orbifold. The canonical projection onto the leaf space is a submersion in the category of orbifolds. We prove that the group of all diffeomorphisms of an orbifold is isomorphic to the group of basic automorphisms (in the category of foliations) of the constructed model foliation. In terms of the model foliations necessary and sufficient conditions are found for orbifold to be good. As the application we obtain that every orbifold admitting Cartan geometry of zero curvature is good.