  Let $G$ be a semisimple adjoint group over $\bold C$ and $\bar{G}$ be the De
Concini-Procesi completion of $G$. In this paper, we define a Lagrangian
subvariety $\Lambda$ of the cotangent bundle of $\bar{G}$ such that the
singular support of any character sheaf on $\bar{G}$ is contained in $\Lambda$.
