  We define the notion of connectivity set for elements of any finitely
generated Coxeter group. Then we define an order related to this new statistic
and show that the poset is graded and each interval is a shellable lattice.
This implies that any interval is Cohen-Macauley. We also give a Galois
connection between intervals in this poset and a boolean poset. This allows us
to compute the Mobius function for any interval.
