  We revisit the classical two-dimensional McKay correspondence in two
respects: The first one, which is the main point of this work, is that we take
into account of the multiplicative structure given by the orbifold product;
second, instead of using cohomology, we deal with the Chow motives. More
precisely, we prove that for any smooth proper two-dimensional orbifold with
projective coarse moduli space, there is an isomorphism of algebra objects, in
the category of complex Chow motives, between the motive of the minimal
resolution and the orbifold motive. In particular, the complex Chow ring (resp.
Grothendieck ring, cohomology ring, topological K-theory) of the minimal
resolution is isomorphic to the complex orbifold Chow ring (resp. Grothendieck
ring, cohomology ring, topological K-theory) of the orbifold surface. This
confirms the two-dimensional Motivic Crepant Resolution Conjecture.
