Is there a notion of stable homotopy, spectrum, or a stable homotopy category which corresponds to orbifolds and orbispaces, in the same way that classical stable homotopy theory corresponds to ordinary manifolds and spaces?

I'm not so interested in speculations about what such a thing *might* look like; I can come up with my own speculations. I'm curious whether orbifold theorists have actually come up with such notions before and used them for things.