In this note we apply the Guillén-Navarro descent theorem to define a descent variant of the algebraic K-theory of varieties over a field of characteristic zero, KD(X), which coincides with K(X) for smooth varieties and to prove that there is a natural weight filtration on the groups KD*(X). After a result of Haesemeyer, we deduce that this theory is equivalent to the homotopy algebraic K-theory introduced by Weibel.
Homology, Homotopy and Applications, Vol. 11 (2009), No. 2, pp.5-25.