  In this paper we provide an extension of the theory of descent of
Ginzburg-Rallis- Soudry to the context of essentially self-dual
representations, that is representations which are isomorphic to the twist of
their own contragredient by some Hecke character. Our theory supplements the
recent work of Asgari-Shahidi on the functorial lift from (split and quasisplit
forms of) GSpin(2n) to GL(2n).
