We present a G0W0 approach that is based on the evaluation of the linear response of the actions of the G0 and W0 operators. In this way we avoid sums over empty one-particle orbitals and do not have to explicitly develop the screened Coulomb interaction W0 on a dedicated basis. For a given orbital, the self-energy is found by summing terms relative to a set of points in the real-space simulation cell. This permits us to easily control the ratio of the accuracy to the computational cost. A trivial parallelization strategy allows strong linear scaling up to tens of thousands of computing cores.