C*-algebras associated with integral domains and crossed products by actions on adele spaces

Abstract

We compute the K-theory for C*-algebras naturally associated with rings of integers in number fields.

The main ingredient is a duality theorem for arbitrary global fields. It allows us to identify the crossed product arising from affine transformations on the finite adeles with the analogous crossed product algebra over the infinite adele space.

A correction to this paper is available.