It is proved, that any compact subset K of an interpolation C^m,a-smooth manifold on the distinguished boundary of unit polydisc Uⁿ is a peak set for the algebra of smooth functions A^m-1,a(Uⁿ). Besides, the following interpolation result is obtained: For given f О C^m(Tⁿ) there is F О A^m-1,a(Uⁿ) with F|_K = f|_K. If given f belongs to C^m-1,a(Tⁿ), then the interpolating function F can be chosen from (Uⁿ).