The Steinberg curve

Let E and E' be elliptic curves over C. We construct non-torsion 0-cycles i n the kernel of the Albanese mapping CHU (E x E')(deg) (0) --> E x E', whic h are not detectable by a certain class of cohomology theories, including t he cohomology of the analytic motivic complex involving the dilogarithm fun ction defined by S. Bloch. This is in contrast to the etale version of Bloc h's complex defined by S. Lichtenbaum, which contains the Chow group.