Epsilon dichotomy for twisted linear models

Let E/F be a quadratic extension of local nonarchimedean fields of characteristic zero and let D be a quaternion algebra over F containing E. We study a relation between the existence of twisted linear models on GL n ( D) and the local root numbers.1. Introduction 59 2. Preliminaries 61 3. The geometric side: orbital integrals and smooth transfer 63 4. The spectral side: spherical characters 68 5.The forward direction 76 6.The converse direction 80 Appendix: Ellipticity of supercuspidal representations of G 88