  The half-liberated orthogonal group $O_n^*$ appears as intermediate quantum
group between the orthogonal group $O_n$, and its free version $O_n^+$. We
discuss here its basic algebraic properties, and we classify its irreducible
representations. The classification of representations is done by using a
certain twisting-type relation between $O_n^*$ and $U_n$, a non abelian
discrete group playing the role of weight lattice for $O_n^*$, and a number of
methods inspired from the theory of Lie algebras. We use these results for
showing that the discrete quantum group dual to $O_n^*$ has polynomial growth.
