  Relying on results of Hopkins-Morel, we show that, for $X$ a quasi-projective
variety over a field of characteristic zero, the canonical map $\Omega_n(X)\to
MGL_{2n,n}'(X)$ is an isomorphism. Here $\Omega_*(X)$ is the theory of
algebraic cobordism defined by Levine-Morel, and $MGL_{*,*}'$ is the
Borel-Moore homology version of the theory of algebraic cobordism defined via
the algebraic Thom complex in the Morel-Voevodsky motivic stable homotopy
category.
