We discuss a C*-dynamical system arising from the ring inclusion of the 2x2 integer matrices in the rational ones. The underlying C*-algebra is the reduced C*-algebra of a semidirect product Hecke pair associated to the inclusion, and is closely related to the GL2 − system of Connes and Marcolli. We describe a general procedure for obtaining induced representations of Hecke C*-algebras of semidirect products, and for the particular system we obtain a family of faithful representations. We establish a tensor product decomposition of the fixed-point algebra under a natural group of symmetries, and use this and the family of representations to describe a phase transition for a natural class of KMS-states. (Joint work with M. Laca and S. Neshveyev.)