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In this work we study the quasi-two-body decays $B\to K^*\gamma\toK\pi\gamma$ in the perturbative QCD (PQCD) approach. The two-meson distributionamplitudes (DAs) are introduced to describe the final state interactions of the$K\pi$ pair, which involve the time-like form factors and the Gegenbauerpolynomials. We calculate the CP averaged branching ratios for the decays$B_{(s)}\to K^*\gamma\to K\pi\gamma$. Our results are in agreement with the newupdate data measured by Belle II, which suggests these quasi-two-body decaysare more appropriate to be analyzed in three-body framework than in thetwo-body one. We also predict the direct CP-violation asymmetries for theconsidered decay modes and find that $A_{CP}(B_{u,d}\to K^*\gamma\toK\pi\gamma)$ is small and less than $1\%$ in magnitude, while $A_{CP}(B_{s}\toK^*\gamma\to K\pi\gamma)$ is larger and can arrive at a few percent. Ourpredictions can be tested by the future B meson experiments.

Quasi-two-body decays $B_{(s)}\to K^*\gamma\to K\pi\gamma$ in perturbative QCD approach