Let X be a complex manifold. By homological mirror symmetry one expects an action of the fundamental group of the "moduli space of Kähler structures" of X on the derived category of X. If X is a crepant resolution of a Gorenstein affine toric variety we obtain an action on the derived category of the toric boundary divisor of X which leads to an action on the Grothendieck group of X. This is a joint work with Michel Van den Bergh.