  Let $X$ be a projective variety with an action of a reductive group $G$. Each
ample $G$-line bundle $L$ on $X$ defines an open subset $X^{\rm ss}(L)$ of
semi-stable points. Following Dolgachev and Hu, define a GIT-class as the set
of algebraic equivalence classes of $L'$s with fixed $X^{\rm ss}(L)$. We show
that the GIT-classes are the relative interiors of rational polyhedral convex
cones, which form a fan in the $G$-ample cone. We also study the corresponding
variations of quotients $X^{\rm ss}(L)//G$. This sharpens results of Thaddeus
and Dolgachev-Hu.
