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 20.5fb⁻¹ collected with the CMS detector at the LHC in pp collisions at √s=8TeV. 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.