This question is inspired by this MO question; in turn by this MO; in turn by these MO, MO.

An exotic affine space is an affine variety $V$ whose $\mathbb{C}$-points are diffeomorphic to $\mathbb{R}^{2n}$ yet $V$ is not algebraically isomorphic to $\mathbb{A}^n$. Will Sawin showed in his answer MO that the number of $F_q$ points is the same for fake affine spaces as for non-fake (for generic $q$).

**Question:** Are exotic affine spaces equivalent to affine space in Grothendieck ring of varietes ? Or may be there are some other simple geometric equivalence which is stronger than just point counting and weaker than isomorphism ?

PS

Evgeny Shinder in comments to MO states that " Among nonsingular projective varieties, a fake projective plane or odd-dimensional quadrics have the same point count as projective planes. In the case of a fake projective plane its class in the Grothendieck ring is not L^2 + L + 1 (and in fact not congruent to 1 (mod. L) because it's not stably rational). The class of a quadric is same as [P^n] (using projection from the point). "