Fifteen years ago Bost and Connes constructed a C dynamical system with the Calois group G(Qab /Q) as symmetry group and with phase tran- sition related to properties of L-functions . Since then there have been nu- merous , and only partially succesful , attempts to generalize the system to arbitrary number ﬁelds . A few years ago , in order to extend that con- struction to imaginary quadratic feilds , Connes and Marcolli constructed a GL2 system , an analogue of the BC-system with Q replaced by GL2 (Q). They classiﬁed the KM S states of the system for > 2. Later Laca , Larsen and Neshveyev classiﬁed the KM Sstates for all = 0, 1.