In recent work with Greither, we proved a main conjecture in equivariant Iwasawa theory, refining Wiles´ results on the classical main conjecture over totally real number fields. Via Iwasawa co-descent this permitted us to prove a refinement of the classical Brumer-Stark conjecture (under certain hypotheses.) In joint work with Banaszak, we used these results to construct a family of algebraic Hecke characters for an arbitrary CM number field, generalizing Weil´s Jacobi sum Hecke characters. Further, we used certain special values of these Hecke characters to construct "Stickelberger splitting" maps for the localization sequences in the Quillen K-theory of CM and totally real number fields. We will review these results and constructions and comment on further potential applications to the classical conjectures of Iwasawa and Kummer-Vandiver on class-groups of cyclotomic fields.