  In this note we apply Guillen-Navarro descent theorem, \cite{GN02}, to define
a descent variant of the algebraic $K$-theory of varieties over a field of
characteristic zero, $\mathcal{KD}(X)$, which coincides with $\mathcal{K}(X)$
for smooth varieties. After a result of Haesemeyer, this new theory is
equivalent to the homotopy algebraic $K$-theory introduced by Weibel. We also
prove that there is a natural weight filtration on the groups $KH_\ast(X)$.
