Heavy flavor operator matrix elements at $O(a_s^3)$

The heavy quark effects in deep--inelastic scattering in the asymptotic regime $Q^2 gg m^2$ can be described by heavy flavor operator matrix elements. Complete analytic expressions for these objects are currently known to ${sf NLO}$. We present first results for fixed moments at ${sf NNLO}$. This involves a recalculation of fixed moments of the corresponding ${sf NNLO}$ anomalous dimensions, which we thereby confirm.