  We introduce a new micro-macro decomposition of collisional kinetic equations
in the specific case of the diffusion limit, which naturally incorporates the
incoming boundary conditions. The idea is to write the distribution function
$f$ in all its domain as the sum of an equilibrium adapted to the boundary
(which is not the usual equilibrium associated with $f$) and a remaining
kinetic part. This equilibrium is defined such that its incoming velocity
moments coincide with the incoming velocity moments of the distribution
function. A consequence of this strategy is that no artificial boundary
condition is needed in the micro-macro models and the exact boundary condition
on $f$ is naturally transposed to the macro part of the model. This method
provides an 'Asymptotic preserving' numerical scheme which generates a very
good approximation of the space boundary values at the diffusive limit, without
any mesh refinement in the boundary layers. Our numerical results are in very
good agreement with the exact so-called Chandrasekhar value, which is
explicitely known in some simple cases.
