The stable category $\underline{\sf CM}^{\mathbb Z}(S^G)$, where $S$ is the polynomial ring in $n$ variables and $G< {\sf SL}(n, k)$ is finite, has been studied for different gradings. Assuming that the skew-group algebra $S\#G$ is endowed with the grading structure of a bimodule Calabi-Yau algebra of Gorenstein parameter $1$, Amiot, Iyama and Reiten constructed a triangle equivalence with the derived category of a finite-dimensional algebra. A similar equivalence was also obtained by Iyama and Takahashi provided that $S$ is generated in degree $1$, in which case $S\#G$ has Gorenstein parameter $n$. This result was later generalised to noetherian AS-regular Koszul algebras by Mori and Ueyama. We are interested in understanding the cases where the Gorenstein parameter is arbitrary. In this talk, we will discuss certain silting objects and then specialise to the situation in which the Beilinson algebra is a levelled algebra, giving a generalisation of the equivalence of Mori and Ueyama.