Abstract We compute the stringy Chow ring of a general Deligne–Mumford stack of the form X/G for a smooth variety X and diagonalizable group scheme G, working over a base field that is not necessarily algebraically closed. We then specialize to the stringy Chow ring of the weighted blow-up of a smooth variety along a smooth center. We explore finite generation properties of this ring.
Kuang et al. (Sat,) studied this question.