The main result of the paper is that the equivariant intersection coho
mology of the semistable points on a complex projective variety, for t
he action of a complex reductive group, may be determined from the equ
ivariant intersection cohomology of the semi-stable points for the act
ion of a maximal torus. It extends the work of Brion who considered th
e smooth case using equivariant cohomology. Equivariant intersection c
ohomology is a theory due to Brylinski and the second author. As an ap
plication, a surprising relation between the intersection cohomology o
f Chow hypersurfaces is established in the last section of the paper.