Isospin breaking by QED interactions plays an important role in the
standard model phenomenology. The lattice provides an ab-initio
framework to compute hadron mass splittings due to QED effects. While
calculations of these effects are already available, the most accurate
results rely on a non-local formulation of QED at finite volume, known
as QED$_L$. In a full first-principle approach, for this formulation,
one would need to show that the violation of locality at finite volume
does not result in subtleties that might generate hard to control
systematic effects. As an alternative programme, in this talk, we
analyse a formulation of QCD coupled to QED on a C*-periodic finite
lattice, which is local. Finite size corrections to charged particle
masses are shown to have a different functional form in our framework
and turn out to be significantly smaller than in QED$_L$. The flavour
and baryon symmetries are discussed both at finite lattice size and in
the approach to the infinite volume limit. Gauge covariant expressions
of electrically charged operators and a formulation of the theory on the
lattice are also presented.