An angular analysis of the decay B0s→K∗0K¯¯¯¯¯∗0 is performed using pp collisions corresponding to an integrated luminosity of 1.0 fb−1 collected by the LHCb experiment at a centre-of-mass energy s√=7 TeV. A combined angular and mass analysis separates six helicity amplitudes and allows the measurement of the longitudinal polarisation fraction f L = 0.201 ± 0.057 (stat.) ± 0.040 (syst.) for the B0s→K∗(892)0K¯¯¯¯¯∗(892)0 decay. A large scalar contribution from the K 0 ∗ (1430) and K 0 ∗ (800) resonances is found, allowing the determination of additional CP asymmetries. Triple product and direct CP asymmetries are determined to be compatible with the Standard Model expectations. The branching fraction B(Bs→K∗(892)0K¯¯¯¯¯∗(892)0) is measured to be (10.8 ± 2.1 (stat.) ± 1.4 (syst.) ± 0.6 (f d /f s )) × 10−6.