  We consider a diffusion equation with highly oscillatory coefficients that
admits a homogenized limit. As an alternative to standard corrector problems,
we introduce here an embedded corrector problem, written as a diffusion
equation in the whole space in which the diffusion matrix is uniform outside
some ball of radius $R$. Using that problem, we next introduce three
approximations of the homogenized coefficients. These approximations, which are
variants of the standard approximations obtained using truncated (supercell)
corrector problems, are shown to converge when $R \to \infty$. We also discuss
efficient numerical methods to solve the embedded corrector problem.
