On the K-theory of the C*-algebra generated by the left regular   representation of an Ore semigroup
  We compute the K-theory of C*-algebras generated by the left regular representation of left Ore semigroups satisfying certain regularity conditions. Our result describes the K-theory of these semigroup C*-algebras in terms of the K-theory for the reduced group C*-algebras of certain groups which are typically easier to handle. Then we apply our result to specific semigroups from algebraic number theory. 
Joachim Cuntz, Siegfried Echterhoff and Xin Li
math.OA math.KT