  We describe new autoequivalences of derived categories of coherent sheaves
arising from what we call $\mathbb P^n$-objects of the category. Standard
examples arise from holomorphic symplectic manifolds. Under mirror symmetry
these autoequivalences should be mirror to Seidel's Dehn twists about
lagrangian $\mathbb P^n$ submanifolds.
  We give various connections to spherical objects and spherical twists, and
include a simple description of Atiyah and Kodaira-Spencer classes in an
appendix.
