  Let k be a field. Let K_0(V_k) denote the quotient of the free abelian group
generated by the geometrically reduced varieties over k, modulo the relations
of the form [X]=[X-Y]+[Y] whenever Y is a closed subvariety of X. Product of
varieties makes K_0(V_k) into a ring. We prove that if the characteristic of k
is zero, then K_0(V_k) is not a domain.
