  We extend the notion of induced conjugacy classes in reductive groups,
introduced by Lusztig and Spaltenstein for unipotent classes, to arbitrary
classes. We study properties of equivariant fibrations of prehomogeneous affine
spaces, especially the existence of relative invariants. We also detect
prehomogeneous affine spaces as subquotients of canonical parabolic subgroups
attached to elements of reductive groups in the sense of Jacobson-Morozov.
These results are prerequisites for making the geometric expansion of the
Arthur-Selberg trace formula more explicit.
