Inertial Chow rings and a new asymptotic product

For any toric Deligne-Mumford stack X and equivariant vector bundle V , we can de ne an two associative inertial products. We give a ring presentation for the inertial Chow ring of X under each of these products and compute these rings in the toric case. In particular, we make explicit distinctions between the contributions of the inertia of X and of the products themselves. We further show the existence of a new associative product on the inertia of X in which the rank of V asymptotically approaches in nity, and we compute its Chow ring.