Hyperplane arrangements and K-theory

We study the Z2-equivariant K-theory of M(A), where M(A) is the complement of the complexification of a real hyperplane arrangement, and Z2 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.