  Let $G$ be a connected reductive group, $T$ a maximal torus of $G$, and $N$
the normalizer of $T$ in $G$. In this paper we study the connection between the
derived category of l-adic sheaves on the stack $[Lie(T)/N]$ and the derived
category of $l$-adic sheaves on $[Lie(G)/G]$.
