Equivariant K-theory, affine Grassmannian and perfection Löwit, Jakub equivariant algebraic K-theory perfection in positive characteristic affine Grassmannian affine Schubert varieties Dennis trace map equivariant Hochschild homology fixed-point schemes toric varieties ddc:500 We study torus-equivariant algebraic K-theory of affine Schubert varieties in the perfect affine Grassmannians over Fp. We further compare it to the torus-equivariant Hochschild homology of perfect complexes, which has a geometric description in terms of global functions on certain fixed-point schemes. We prove that Fp-linearly, this comparison is an isomorphism. Our approach is quite constructive, resulting in new computations of these K-theory rings. We establish various structural results for equivariant perfect algebraic K-theory on the way; we believe these are of independent interest. EMS Press 2026 info:eu-repo/semantics/article doc-type:article text http://purl.org/coar/resource_type/c_2df8fbb1 https://research-explorer.ista.ac.at/record/22693 Löwit J. Equivariant K-theory, affine Grassmannian and perfection. <i>Documenta Mathematica</i>. 2026. doi:<a href="https://doi.org/10.4171/dm/1064">10.4171/dm/1064</a> eng info:eu-repo/semantics/altIdentifier/doi/10.4171/dm/1064 info:eu-repo/semantics/altIdentifier/issn/1431-0635 info:eu-repo/semantics/altIdentifier/e-issn/1431-0643 info:eu-repo/semantics/altIdentifier/arxiv/2409.18925 info:eu-repo/semantics/openAccess