  We construct a contractive, idempotent, MASA bimodule map on B(H), whose
range is not a ternary subalgebra of B(H). Our method uses a crossed-product to
reduce the existence of such an idempotent map to an analogous problem about
the ranges of idempotent maps that are equivariant with respect to a group
action and Hamana's theory of G-injective envelopes.
