  This paper has two parts. In the first part we construct arithmetic models of
Bost-Connes systems for arbitrary number fields, which has been an open problem
since the seminal work of Bost and Connes [3]. In particular our construction
shows how the class field theory of an arbitrary number field can be realized
through the dynamics of a certain operator algebra. This is achieved by working
in the framework of Endomotives, introduced by Connes, Marcolli and Consani
[5], and using a classification result of Borger and de Smit [1] for certain
{\Lambda}-rings in terms of the Deligne-Ribet monoid. Moreover the uniqueness
of the arithmetic model is shown by Sergey Neshveyev in an appendix. In the
second part of the paper we introduce a base-change functor for a class of
algebraic endomotives and construct in this way an algebraic refinement of a
functor from the category of number fields to the category of Bost-Connes
systems, constructed recently by Laca, Neshveyev and Trifkovic [13].
