Let K be an algebraic number field, and let G_K be the group of K-rational points of a simply connected simple linear algebraic group G defined over K. We construct a new family of irreducible unitary representations of G_K as follows. It is well known that G_K embeds diagonally as a lattice in G_A, where A is the ring of adèles of K. Let p\pi be an irreducible unitary representation of G_A. We show that p|_GK\pi\vert_{G_K}, the restriction of p\pi to G_K, is irreducible and that p\pi is determined by p|_GK\pi\vert_{G_K} up to unitary equivalence. Many of these restrictions are not in the support of the regular representation of G_K.