The class of the affine line is a zero divisor in the Grothendieck ring:   via $G_2$-Grassmannians
  Motivated by [Bor] and [Mar], we show the equality $\left([X] - [Y]\right) \cdot [\mathbb{A}^1] = 0$ in the Grothendieck ring of varieties, where $(X, Y)$ is a pair of Calabi-Yau 3-folds cut out from the pair of Grassmannians of type $G_2$. 
Atsushi Ito, Makoto Miura, Shinnosuke Okawa, Kazushi Ueda
math.AG