Weights for $\mathrm{K}$-motives on stacks

Abstract

We construct the Chow weight structure on a full subcategory of the category of $\mathrm{K}$-motives over a tame quotient stack in characteristic zero as defined by Hoyois. We also prove that in a quite general case, this full subcategory is exactly the category of geometric $\mathrm{K}$-motives. We apply this to give a partial Springer decomposition in the context of $\mathrm{K}$-motives.