  The additive invariants of an algebraic variety is calculated in terms of
those of the fixed point set under the action of additive and multiplicative
groups, by using Bialynicki-Birula's fixed point formula for a projective
algebraicset with a G_m-action or G_a-action.
  The method is also generalized to calculate certain additive invariants for
Chow varieties. As applications, we obtain the Hodge polynomial of Chow
varieties in characteristic zero and the number of points for Chow varieties
over finite fields.
  As applications, we obtain the l-adic Euler-Poincare characteristic for the
Chow varieties of certain projective varieties over an algebraically closed
field of arbitrary characteristic. Moreover, we show that the virtual Hodge
(p,0) and (0,q)-numbers of the Chow varieties and affine group varieties are
zero for all p,q positive.
