Geodesic
The index of Fourier integral operators on manifolds with conical singularities
Izvestiya. Mathematics , Tome 65 (2001) no. 2, pp. 329-355.

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We describe homogeneous canonical transformations of the cotangent bundle of a manifold with conical singular points and compute the index of an elliptic Fourier integral operator obtained by the quantization of such a transformation. The answer involves the index of an elliptic Fourier integral operator on a smooth manifold and the residues of the conormal symbol. 
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V. E. Nazaikinskii; B. Schulze; B. Yu. Sternin. The index of Fourier integral operators on manifolds with conical singularities. Izvestiya. Mathematics , Tome 65 (2001) no. 2, pp. 329-355. http://geodesic.mathdoc.fr/item/IM2_2001_65_2_a3/

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