  To an arbitrary variety over a field of characteristic zero, we associate a
complex of Chow motives, which is, up to homotopy, unique and bounded. We
deduce that any variety has a natural Euler characteristic in the Grothendieck
group of Chow motives. We show that the cohomology with integer coefficients of
any singular variety over the complex numbers has a natural weight filtration.
We define algebraic K-theory with "compact supports".
