  We study an analogue of the Brauer-Manin obstruction to the local-global
principle for embedding problems over global fields. We will prove the
analogues of several fundamental structural results. In particular we show that
the (algebraic) Brauer-Manin obstruction is the only one to weak approximation
when the embedding problem has abelian kernel. As a part of our investigations
we also give a new, elegant description of the Tate duality pairing and prove a
new theorem on the cup product.
