  If we have a braid group acting on a derived category by spherical twists,
how does a lift of the longest element of the symmetric group act? We give an
answer to this question, using periodic twists, for the derived category of
modules over a symmetric algebra. The question has already been answered by
Rouquier and Zimmermann in a special case. We prove a lifting theorem for
periodic twists, which allows us to apply their answer to the general case.
  Along the way we study tensor products in derived categories of bimodules. We
also use the lifting theorem to give new proofs of two known results: the
existence of braid relations and, using the theory of almost Koszul duality due
to Brenner, Butler, and King, the result of Rouquier and Zimmermann mentioned
above.
