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A set of quantum states, dynamically related to the classical periodic orbitsof a chaotic map, is used as a basis in which the description of theeigenstates of its quantum version is greatly simplified. This set can beimproved with the inclusion of short time propagation along the stable andunstable manifolds of the periodic orbits resulting in a construction similarto the scar functions of Vergini (Jour. Phys. A \textbf{33}, (2000) 4709). Theaverage participation ratio is used to quantify the quality of the basis.

A periodic orbit basis for the Quantum Baker Map