On indecomposable elements of K1 of a product of elliptic curves

Let E-1, E-2 be elliptic curves with good reduction over a local field k of residue characteristic p. Let X be the smooth projective model of E-1 x E-2 over the ring of integers of k. We show that Ker(C H-2(X) --> C H-2 (E-1 x E-2)) is a finite p-group, by giving a new construction of indecomposable elements of H-Zar(1)(E-1 x E-2, K-2). As an application we show that the prime to p part of the torsion subgroup of C H-2(E-1 x E-2) is finite.