  The classical McKay correspondence for finite subgroups $G$ of $\SL(2,\C)$
gives a bijection between isomorphism classes of nontrivial irreducible
representations of $G$ and irreducible components of the exceptional divisor in
the minimal resolution of the quotient singularity $\A^2_\C/G$. Over non
algebraically closed fields $K$ there may exist representations irreducible
over $K$ which split over $\bar{K}$. The same is true for irreducible
components of the exceptional divisor. In this paper we show that these two
phenomena are related and that there is a bijection between nontrivial
irreducible representations and irreducible components of the exceptional
divisor over non algebraically closed fields $K$ of characteristic 0 as well.
