For cellular toroidal embeddings of a complex reductive group, the equivariant topological K-ring is described explicitly as an algebra over the equivariant K-ring of the wonderful compactification.
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Equivariant $K$-theory of cellular toroidal embeddings
For cellular toroidal embeddings of a complex reductive group, the equivariant topological K-ring is described explicitly as an algebra over the equivariant K-ring of the wonderful compactification.