Résumé
We propose a generalisation of the Jacquet-Langlands correspondence to the
whole Grothendieck group of finite lenght admissible representations. As an
application we prove some particular cases of the global Jacquet-Langlands
correspondence, and that a class of representations of a inner form of GL_n
over a p-adic field is unitarisable, which agree with some conjecture of Tadic.