Singularity categories via McKay quivers with potential

In 2018, Kalck-Yang showed that the singularity categories associated with 3-dimensional Gorenstein quotient singularities are (up to direct summands) triangle equivalent to small cluster categories associated with McKay quivers with potential. We introduce (graded) McKay quivers with potential and generalize Kalck-Yang's theorem to arbitrary dimensions. Moreover, we characterize the singularity categories in the non-Gorenstein case. More generally, singularity categories have a relative variant known as categories of Cohen-Macaulay modules. We also prove the relative variant of the structure theorem.