K-theory of certain additive categories associated with varieties

Let K0(Vark) be the Grothendieck group of varieties over a field k. We construct an exact category, denoted Add(Vark)S, such that there is a surjection K0(Vark)→K0(Add(Vark)S).If we consider only zero dimensional varieties, then this surjection is an isomorphism. Like K0(Vark), the group K0(Add(Vark)S) is also generated by isomorphism classes of varieties,and we construct motivic measures on K0(Add(Vark)S) including the Euler characteristic if k=C, and point counting measures and the zeta function if k is finite.