  I will present an explicit formula for the intersection indices of the Chern
classes of an arbitrary reductive group with hypersurfaces. This formula has
the following applications. First, it allows to compute explicitly the Euler
characteristic of complete intersections in reductive groups. Second, for any
regular compactification of a reductive group, it computes the intersection
indices of the Chern classes of the compactification with hypersurfaces. The
formula is similar to the Brion--Kazarnovskii formula for the intersection
indices of hypersurfaces in reductive groups. The proof uses an algorithm of De
Concini and Procesi for computing such intersection indices. In particular, it
is shown that this algorithm produces the Brion--Kazarnovskii formula.
