C*-algebras associated with endomorphisms of groups

In 2002 Ilan Hirshberg defined a C*-algebra associated with endomorphisms of abelian groups with finite cokernel. In fact it was a starting point of new constructions associating C*-algebras to simple objects like groups semigroups and rings. In this book we present a natural continuation of that work we construct the same C*-algebra for endomorphisms with infinite cokernel. We use the subset structure of the group to index interesting projections in the C*-algebra and present interesting connections with the semigroup C*-algebras defined by Xin Li. We also calculate some K-groups associated to such constructions.