Lifting of characters for nonlinear simply laced groups

One aspect of the Langlands program for linear groups is the lifting of characters, which relates virtual representations on a group $G$ with those on an endoscopic group for $G$. The goal of this paper is to extend this theory to nonlinear two-fold covers of real groups in the simply laced case. Suppose $\widetilde G$ is a two-fold cover of a real reductive group $G$. A representation of $\widetilde G$ is called genuine if it does not factor to $G$. The main result is that there is an operation, denoted Lift$_G^{\widetilde G}$, taking a stable virtual character of $G$ to a virtual genuine character of $\widetilde G$, and Lift$_G^{\widetilde G}(\Theta_\pi)$ may be explicitly computed if $\pi$ is a stable sum of standard modules.