  We prove a full global Jacquet-Langlands correspondence between GL(n) and
division algebras over global fields of non zero characteristic. If $D$ is a
central division algebra of dimension $n^2$ over a global field $F$ of non zero
characteristic, we prove that there exists an injective map from the set of
automorphic square integrable representations of the multiplicative group of
$D$ to the set of automorphic square integrable representations of GL_n(F),
compatible at all places with the local Jacquet-Langlands correspondence for
unitary representations. We characterize the image of the map. As a consequence
we get multiplicity one and strong multiplicity one theorems for the
multiplicative group of D.
