  Suppose $G$ is a connected complex semisimple group and $W$ is its Weyl
group. The lifting of an element of $W$ to $G$ is semisimple. This induces a
well-defined map from the set of elliptic conjugacy classes of $W$ to the set
of semisimple conjugacy classes of $G$. In this paper, we give a uniform
algorithm to compute this map. We also consider the twisted case.
