  Using a construction closely related to Waldhausen's
$S_\bullet$-construction, we produce a spectrum $K(\mathbf{Var}_{/k})$ whose
components model the Grothendieck ring of varieties (over a field $k$) $K_0
(\mathbf{Var}_{/k})$. We then produce liftings of various motivic measures to
spectrum-level maps, including maps into Waldhausen's $K$-theory of spaces
$A(\ast)$ and to $K(\mathbf{Q})$. We end with a conjecture relating
$K(\mathbf{Var}_{/k})$ and the doubly-iterated $K$-theory of the sphere
spectrum.
