Symmetric \(K\)-theory spectra of \(C^*\)-categories (Q1598942)

A \(C^*\)-category is a Banach category equipped with an involution satisfying the \(C^*\)-property. The author discusses in detail \(K\)-theory groups and \(K\)-theory spectra associated to \({\mathbb Z}_2\)-graded \(C^*\)-categories. He proves a version of the Bott periodicity theorem for the \(K\)-theory of \(C^*\)-categories and uses it to define a functor associating a symmetric \(K\)-theory spectrum to a \(C^*\)-category. He also shows that the exterior product of \(K\)-groups can be expressed in terms of the smash product of symmetric spectra.