[en] We present the first four-flavour lattice calculation of the leading-order hadronic vacuum-polarisation contribution to the anomalous magnetic moment of the muon, a^hvp_μ, and the hadronic running of the QED coupling constant, Δα^hvp_QED(Q²). In the heavy sector a mixed-action setup is employed. The bare quark masses are determined from matching the K- and D-meson masses to their physical values. Several light quark masses are used in order to yield a controlled extrapolation to the physical pion mass by utilising a recently proposed improved method. We demonstrate that this method also works in the four-flavour case.