Rigidity for equivariant \(K\)-theory (Q1046545)

The authors extend the classical rigidity results for algebraic \(K\)-theory with torsion coefficients to the equivariant setting of linear algebraic group actions. These results concern rigidity for rational points, field extensions, and Hensel local rings. Let \(G\) be a linear algebraic group over an infinite field \(k\). Let \(V\) be a \(G\)-equivariant separated \(k\)-scheme of finite type. Let \(n>0\) be prime to the characteristic of \(k\). It is shown that \(K_*(V\times_k - ;\mathbb Z/n)\) defines a functor `with weak transfers' on the category of smooth quasi projective \(k\)-schemes. The rigidity results follow.