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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, and a number of methods inspired from the theory of Lie algebras. We use these results for showing that...