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In part I of this work we studied the spaces of real algebraic cycles on a complex projective space P(V), where V carries a real structure, and completely determined their homotopy type. We also extended some functors in K-theory to algebraic cycles, establishing a direct relationship to characteristic classes for the classical groups, specially Stiefel-Whitney classes. In this sequel, we establish corresponding results in the case where V has a quaternionic structure. The determination of thedoi:10.2140/gt.2005.9.1187 fatcat:mrbo5msjd5gdfmq44kqdb5qrxu