Hyperplane arrangements and K-theory

We study the Z 2 -equivariant K-theory of M ( A ) , where M ( A ) is the complement of the complexification of a real hyperplane arrangement, and Z 2 acts on M ( A ) by complex conjugation. We compute the rational equivariant K- and KO-rings of M ( A ) , and we give two different combinatorial descriptions of a subring Line ( A ) of the integral equivariant KO-ring, where Line ( A ) is defined to be the subring generated by equivariant line bundles.