2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/144958Given a smooth stacky Calabi-Yau hypersurface X in a weighted projective space, we consider the functor G which is the composition of the following two autoequivalences of D^b(X): the first one is induced by the spherical object O_X, while the second one is tensoring with O_X(1). The main result of the paper is that the composition of G with itself w times, where w is the sum of the weights of the weighted projective space, is isomorphic to the autoequivalence "shift by 2". The proof also involves the construction of a Beilinson type resolution of the diagonal for weighted projective spaces, viewed as smooth stacks.19 pages; minor modifications; accepted by J. Geom. PhysAlgebraic Geometry18E30, 14J32, 14A20text