CCAST, World Lab, Beijing 100080, Peoples R China
; CAS, Inst High Energy Phys, Beijing 100049, Peoples R China
; Chinese Acad Sci, Grad Sch, Beijing 100864, Peoples R China
We study the charmless rare decays B -> (KK*)-K-* within the perturbative QCD picture. We calculate not only factorizable and nonfactorizable diagrams, but also annihilation ones. Our predictions are the following: The longitudinal polarization fraction vary from 75% to 99% depending on channels, the branching ratios are of order 10(-7) for B-0(B over-bar(0))-> (KK)-K-*0 over-bar(*0) and B+/--> K*+/-K over-bar(*0)(K-*0), much bigger than that for B-0(B over-bar(0))-> K*+Kover-bar*-(10(-8)). The direct CP asymmetry in B+/--> K*+/-Kover-bar*0(K-*0) and B-0(B over-bar(0))-> K*+K*- is about -15% and -65% if we choose alpha(phi(2)) as 95 degrees. The direct CP violation in B-0(B over-bar(0))-> (KKover-bar*0)-K-*0 decays is negligible if there is not strong final state interactions. Our predictions will be tested in the future B experiments.