  Let B be a real hyperplane arrangement which is stable under the action of a
Coxeter group W. Then B acts naturally on the set of chambers of B. We assume
that B is disjoint from the Coxeter arrangement A=A(W) of W. In this paper, we
show that the W-orbits of the set of chambers of B are in one-to-one
correspondence with the chambers of C=A\cup B which are contained in an
arbitrarily fixed chamber of A. From this fact, we find that the number of
W-orbits of the set of chambers of B is given by the number of chambers of C
divided by the order of W. We will also study the set of chambers of C which
are contained in a chamber b of B. We prove that the cardinality of this set is
equal to the order of the isotropy subgroup W_b of b. We illustrate these
results with some examples, and solve an open problem in Kamiya, Takemura and
Terao [Ranking patterns of unfolding models of codimension one, Adv. in Appl.
Math. (2010)] by using our results.
