  For an effective Cartier divisor D on a scheme X we may form an nth root
stack. Its derived category is known to have a semiorthogonal decomposition
with components given by D and X. We show that this decomposition is
2n-periodic. For n=2 this gives a purely triangulated proof of the existence of
a known spherical functor, namely the pushforward along the embedding of D. For
n>2 we find a higher spherical functor in the sense of recent work of
Dyckerhoff, Kapranov and Schechtman. We use a realization of the root stack
construction as a variation of GIT, which may be of independent interest.
