The Steinberg curve

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