A group W is said to have property FA_n if every action of W by isometries on an n-dimensional CAT(0) cell complex has a global fixed point. We construct a complex on which a Coxeter group W acts by cellular isometries without global fixed points, and show that under certain combinatorial conditions, complexes constructed in this way are CAT(0). We then construct several infinite classes of Coxeter groups which have property FA_2 but not property FA_3. / text