The ideal structure of the Hecke C*-algebra of Bost and Connes

We compute explicitly the primitive ideal space of the Bost-Connes Hecke C* -algebra by embedding it as a full corner in a transformation group C*-alge bra and applying a general theorem of Williams. This requires the computati on of the quasi-orbit space for the action of Q(+)* on the space A(f) of fi nite adeles. We then carry out a similar computation for the action of Q* o n the space A = A(f) x R of full adeles.