Parallel to equivariant A-theory is the theory of equivariant cobordisms on a G-manifold M. This theory becomes rather subtle when you try to explain how it is a functor along equivariant manifolds and equivariant smooth embeddings. In this talk, we show how to address this functoriality in a satisfactory way, producing a geometric model for the equivariant Whitehead space. As a consequence, we get a splitting on the stable space of equivariant h-cobordisms, parallel to the tom Dieck-style splitting on equivariant A-theory.