We present parameter-free calculations of the quasiparticle band structure of systems described by huge supercells. They are based on a pseudopotential–plane-wave method to calculate the electronic structure in the ground state. All-electron wave functions are constructed using the projector-augmented wave method. The electronic self-energy is calculated within the GW approximation using an efficient approach to the screening. It includes a simplified treatment of dynamical and local-field effects. The approach is carefully tested by computing the quasiparticle band structure of group-IV semiconductors within nonprimitive unit cells containing 216 atoms. The success of the method is demonstrated by the calculation of the electronic structure of Ge and Si nanocrystallites embedded in a SiC matrix.