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In $K$-Theory, actually also in equivariant cohomology theory, there exists a useful theorem as known Borel-Hsiang-Atiyah-Segal Localization theorem. For $K$-Theory Theorem: Let $G$ be a compact Lie ...

I am trying to compute the $G$-theory groups of the ring $k[x,y]/(xy)$ for any field $k$. What I have tried so far are two approaches. Approach 1: Use the $G$-theory localization sequence for $k[x,y]/(...

Let $B$ be an additive category (a small one; one can assume that it is a $\mathbb{Q}$-category, yet not much else is known about it). Given a set of objects $S$ of $K^b(B)$ (or $K(B)$), I consider ...