Abstract
Let F=K be an abelian extension of number G(F=K){equivariant L{functions. Using results of Greither{Popescu (19) on the Brumer{Stark conjecture we construct l{adic imprimitive versions of these characters, for primes l > 2. Further, the special values of these l{adic Hecke characters are used to construct G(F=K){equivariant Stickelberger{splitting maps in the Quillen localization sequence for F, extending the results obtained in (1) for K = Q. We also apply the Stickelberger{splitting maps to construct special elements in K2n(F)l and analyze the Galois module structure of the group D(n)l of divisible elements in K2n(F)l. If n is odd, l - n, and F = K is a fairly general totally real number eld, we study the cyclicity of D(n)l in relation to the classical conjecture of Iwasawa on class groups of cyclotomic elds
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