The angular distributions and the differential branching fraction of the decay B0→K⁎(892)0μ+μ− are studied using data corresponding to an integrated luminosity of 20.5 fb −1 collected with the CMS detector at the LHC in pp collisions at s=8 TeV . From 1430 signal decays, the forward–backward asymmetry of the muons, the K⁎(892)0 longitudinal polarization fraction, and the differential branching fraction are determined as a function of the dimuon invariant mass squared. The measurements are among the most precise to date and are in good agreement with standard model predictions.