Abstract
Let k be a field of characteristic zero. For a linear algebraic group G over k acting on a scheme X , we define the equivariant algebraic cobordism of X and establish its basic properties. We explicitly describe the relation of equivariant cobordism with equivariant Chow groups, K -groups and complex cobordism. We show that the rational equivariant cobordism of a G -scheme can be expressed as the Weyl group invariants of the equivariant cobordism for the action of a maximal torus of G . As applications, we show that the rational algebraic cobordism of the classifying space of a complex linear algebraic group is isomorphic to its complex cobordism.
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