cdh descent in equivariant homotopy \(K\)-theory (Q2186945)

Summary: We construct geometric models for classifying spaces of linear algebraic groups in \(G\)-equivariant motivic homotopy theory, where \(G\) is a tame group scheme. As a consequence, we show that the equivariant motivic spectrum representing the homotopy \(K\)-theory of \(G\)-schemes (which we construct as an \(E_\infty \)-ring) is stable under arbitrary base change, and we deduce that the homotopy \(K\)-theory of \(G\)-schemes satisfies cdh descent.