Baire classes of strongly affine functions on simplices and on C⁎-algebras

For each n∈ω, n≥2, we construct a metrizable simplex X and a strongly affine function of Baire class n on X that is not of affine class n. As a corollary we obtain a separable C⁎-algebra E such that, for each n∈ω, n≥2, the n-th Baire class of E⁎⁎ does not coincide with the n-th intrinsic Baire class of E⁎⁎.