A remark on \(K_ 0\) of crystallographic groups
Let \(\Gamma\) be a crystallographic group. F. Quinn proved a conjecture of the author and W. C. Hsiang: \(K_ 0({\mathbb{Q}} \Gamma)\simeq H_ 0({\mathbb{R}}^ n/\Gamma,\kappa_ 0)\), where \(\kappa_ 0\) denotes the coefficient sheaf on \({\mathbb{R}}^ n/\Gamma\) whose stalk over \(x\Gamma\) is \(K_ 0({\mathbb{Q}} F_ x)\), \(F_ x\) denotes the finite isotropy subgroup of \(\Gamma\) fixing \(x\in {\mathbb{R}}\) and \(x\Gamma\) denotes the orbit of x under \(\Gamma\). In this paper the author gives a counterexample to a naive extension of this conjecture to the integral group ring.
scientific article; zbMATH DE number 4012856