Endoscopy for Mp(2n, [inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="01i" /])

Building on the work of J. Adams on certain dual pair correspondences involving Mp(2n, [inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="02i" /]), and Langlands functoriality for these correspondences, we obtain a theory of endoscopy for the nonlinear group Mp(2n, [inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="03i" /]). Following Shelstad's work for linear groups, we define the endoscopic groups of Mp(2n, [inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="04i" /]), prove the transfer of orbital integrals and the functoriality of the dual lifting of characters.