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The main result of this paper is to establish the weak* completelycontractive approximation property (w*CCAP) for the q-Gaussian algebras for allvalues of q \in [-1, 1] and any number of generators. We use this to establishthat the q-Gaussian algebras are strongly solid in the sense of Popa and Ozawafor q \in (-1, 1).

Strong Solidity of the q-Gaussian Algebras for all -1 < q < 1