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We prove that any spherical representation of the free group 𝔽 weakly contains the regular representation. Moreover C π∗, the C∗-algebra associated with the spherical representation π, is a compact extension of the reduced C∗-algebra of 𝔽. We also show that the standard projection onto radial functions admits extensions to C π∗ for a class of representations π of 𝔽 which includes spherical representations, as well as the regular representation and the universal representation.