Fix a field $k$. The Grothendieck ring $K_0(\mathrm{Var}_k)$ of varieties over $k$ is defined as the quotient of the free abelian group on isomorphism classes of algebraic varieties by the scissor relation. The notation suggests that there might be higher $K$-groups $K_i(\mathrm{Var}_k)$ as well, but naive attempt at defining such an object fails as $K_0(\mathrm{Var})$ is not defined as $K_0$ of an exact additive category. Is there a reasonable definition of these groups nonetheless?