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Strong flatness properties are established for a large class of functional-analytic rings including all C*-algebras. This is later used to prove that all those rings satisfy excision in Hochschild and in cyclic homology over almost arbitrary rings of coefficients and that, for stable C*-algebras, the Hochschild and cyclic homology groups defined over an arbitrary coefficient ring k subset C of complex numbers (e.g., k = Z or Q) vanish in all dimensions.
