  We prove a general theorem that gives a non trivial relation in the group of
derived autoequivalences of a variety (or stack) X, under the assumption that
there exists a suitable functor from the derived category of another variety Y
admitting a full exceptional sequence. Applications include the case in which X
is Calabi-Yau and either X is a hypersurface in Y (this extends a previous
result by the author and R.L. Karp, where Y was a weighted projective space) or
Y is a hypersurface in X. The proof uses a resolution of the diagonal of Y
constructed from the exceptional sequence.
