Maybe this belongs in aspaces.tex instead.
Matthias conversation 4 Feb 2011: Weil-etale cohomology should have projective bundle formula. Not sure about Zariski descent. But there should be a cycle class map, possible factoring over the etale cycle class map. Homotopy invariance fails for the same reason that it fails in etale cohomology with Z-coeffs.
nLab page on Weil-etale stuff