  This paper develops a formalism of endoscopy for the metaplectic group. We
define the notions of stable conjugacy, elliptic endoscopic groups,
correspondence of semisimple geometric conjugacy classes and the transfer
factors in this setting, then we establish the transfer of antigenuine orbital
integrals. Under the hypothesis that the residual characteristic of F is
sufficiently large, the fundamental lemma for the units of the spherical Hecke
algebra also holds. This generalizes the prior works of J. Adams and D. Renard
for real metaplectic groups. Our approach is based on Harish-Chandra's descent
method and the non-standard endoscopy on Lie algebras.
