K-theory of ghostly ideals for ℓp-coarsely embeddable spaces

Ghostly ideals are among the most mysterious objects in coarse index theory. In this paper we show that if a metric space X with bounded geometry admits a coarse embedding into an ℓp-space (1≤p<∞), then the canonical inclusion from any geometric ideal to the corresponding ghostly ideal induces an isomorphism in K-theory. As consequences, we deduce that such spaces satisfy the relative coarse Baum-Connes conjectures introduced in [12], as well as the operator norm localization property for finite rank projections (ONLPFin) as introduced in [1].