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Equivariant algebraic K-theory of affine space
In fact, just like in the case of non-equivariant algebraic $K$-theory, there is a homotopy-invariance for equivariant $K$-theory (of nonsingular varieties). … (The general statement is that when $f\colon X \to Y$ is a $G$-equivariant affine bundle, there is an isomorphism $$f^*\colon G^G_*(Y) \to G^G_*(X),$$ where $G^G_*$ denotes equivariant $K$-theory of coherent …