  We calculate the branching ratios and CP-violating asymmetries for $B^0 \to
K^{0} \ov K^{*0}$, $\ov K^{0} K^{*0}$, $K^+ K^{*-}$, $K^- K^{*+}$, and $B^+\to
K^+ \ov K^{*0}$ and $ \ov K^0 K^{*+} $ decays by employing the low energy
effective Hamiltonian and the perturbative QCD (pQCD) factorization approach.
The theoretical predictions for the branching ratios are $Br(B^0/\ov B^0 \to
K^{\pm} K^{*\mp}) \approx 7.4 \times 10^{-8}$, $Br(B^0/\ov B^0 \to K^{0} \ov
K^{*0}(\ov K^{0} K^{*0})) \approx 19.6 \times 10^{-7}$, $Br(B^+\to K^+ \ov
K^{*0}) \approx 3 \times 10^{-7}$ and $Br(B^+\to K^{*+} \ov K^0) \approx 18.3
\times 10^{-7}$, which are consistent with currently available experimental
upper limits. We also predict large CP-violating asymmetries in these decays:
$A_{CP}^{dir}(K^\pm \ov K^{*0})\approx -20 %$, $A_{CP}^{dir}(K^{*\pm} \ov
K^0)\approx -49%$, which can be tested by the forthcoming B meson experiments.
