  We introduce a self-consistent microscopic theoretical framework for
modelling the process of electron capture on nuclei in stellar environment,
based on relativistic energy density functionals. The finite-temperature
relativistic mean-field model is used to calculate the single-nucleon basis and
the occupation factors in a target nucleus, and $J^{\pi} = 0^{\pm}$, $1^{\pm}$,
$2^{\pm}$ charge-exchange transitions are described by the self-consistent
finite-temperature relativistic random-phase approximation. Cross sections and
rates are calculated for electron capture on 54,56Fe and 76,78Ge in stellar
environment, and results compared with predictions of similar and complementary
model calculations.
