Inertial Chow rings of toric stacks

For any vector bundle V on a toric Deligne-Mumford stack the formalism of Edidin et al. (Ann K-theory 1(1):85-108, 2016) defines two inertial products and on the Chow group of the inertia stack. We give an explicit presentation for the integral and Chow rings, extending earlier work of Borisov et al. (J Am Math Soc 18(1):193-215, 2005) and Jiang and Tseng (Math Z 264(1):225-248, 2010) in the orbifold Chow ring case, which corresponds to . We also describe an asymptotic product on the rational Chow group of the inertia stack obtained by letting the rank of the bundle V go to infinity.