  The reflection length of an element of a Coxeter group is the minimal number
of conjugates of the standard generators whose product is equal to that
element. In this paper we prove the conjecture of McCammond and Petersen that
reflection length is unbounded in any non-affine Coxeter group. Among the tools
used, the construction of word-hyperbolic quotients of all minimal non-affine
Coxeter groups might be of independent interest.
