Algebraic K-theory of a torus is naturally equivalent to the Galois-equivariant homology of its character-lattice torus with equivariant K-theory coefficients.
Chow rings of quasi-split geometrically almost simple algebraic groups
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abstract
We compute the Chow ring of a quasi-split geometrically almost simple algebraic group assuming the coefficients to be a field. This extends the classical computation for split groups done by Kac to the non-split quasi-split case. For the proof we introduce and study equivariant conormed Chow rings, which are well adapted to the study of quasi-split groups and their homogeneous varieties.
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On the K-theory of algebraic tori
Algebraic K-theory of a torus is naturally equivalent to the Galois-equivariant homology of its character-lattice torus with equivariant K-theory coefficients.