A Brumer–Stark conjecture for non-abelian Galois extensions

Let K/kK/k be an abelian extension of number fields. The Brumer–Stark conjecture predicts that a group ring element constructed from special values of L  -functions associated to K/kK/k annihilates the ideal class group of K. Moreover it specifies that the generators obtained have special properties. The aim of this article is to state and study a generalization of this conjecture to non-abelian Galois extensions that is, in spirit, very similar to the original conjecture.