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.