For any vector bundle $V$ on a toric Deligne-Mumford stack $\ix$ the formalism of \cite{ EJK:16} defines two intertial products $\star_{ V^{ +}}$ and $\star_{ V^{ -}}$ on the Chow group of the inertia stack. We give an explicit presentation for the integral $\star_{ V^+}$ and $\star_{ V^-}$ Chow rings, extending earlier work of Boris-Chen-Smith \cite{ BCS:05} and Jiang-Tsen \cite{ JiTs:10} in the orbifold Chow ring case, which corresponds to $V = 0$. We also describe an { \em asymptotic} product on the rational Chow group of the inertia stack obtained by letting the rank of the bundle $V$ go to infinity.
Categories: math.AG