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These notes are the first chapter of a monograph, dedicated to a detailedproof of the equivariant index theorem for transversally elliptic operators. Inthis preliminary chapter, we prove a certain number of natural relations inequivariant cohomology. These relations include the Thom isomorphism inequivariant cohomology, the multiplicativity of the relative Chern characters,and the Riemann-Roch relation between the relative Chern character of the Bottsymbol and of the relative Thom class.

Equivariant relative Thom forms and Chern characters