Abstract: Motivic (co)homology for smooth schemes over a field

is now a well-established theory. This led to the solution to the

Milnor-Bloch-Kato conjecture by Voevodsky and Rost. At present, the

corresponding equivariant theory is developing and attracting many attentions.

In this talk, I will discuss about the equivariant higher Chow groups

defined by Levine-Serp\'e for algebraic varieties equipped with an action

of a finite group. This can be considered as a Borel-Moore homology theory

in the equivariant setting. I will explain how this object relates to

interesting theories such as orbifold Chow ring and equivariant algebraic

K-theory.