Endoscopy for Mp(2n, ℝ)

Building on the work of J. Adams on certain dual pair correspondences involving Mp(2n, ℝ), and Langlands functoriality for these correspondences, we obtain a theory of endoscopy for the nonlinear group Mp(2n, ℝ). Following Shelstad's work for linear groups, we define the endoscopic groups of Mp(2n, ℝ), prove the transfer of orbital integrals and the functoriality of the dual lifting of characters.