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

On Additive invariants of actions of additive and multiplicative groups