  We define algebraic cobordism of classifying spaces, \Omega^*(BG) and
G-equivariant algebraic cobordism \Omega^*_G(-) for a linear algebraic group G.
We prove some properties of the coniveau filtration on algebraic cobordism,
denoted F^j(\Omega^*(-)), which are required for the definition to work. We
show that G-equivariant cobordism satisfies the localization exact sequence. We
calculate \Omega^*(BG) for algebraic groups over the complex numbers
corresponding to classical Lie groups GL(n), SL(n), Sp(n), O(n) and SO(2n+1).
We also calculate \Omega^*(BG) when G is a finite abelian group. A finite
non-abelian group for which we calculate \Omega^*(BG) is the quaternion group
of order 8. In all the above cases, we check that \Omega^*(BG) is isomorphic to
MU^*(BG).
