  We compute the leading terms of the spectral action for a noncommutative
geometry model that has no fermion doubling. The spectral triple describing it,
which is chiral and allows for CP-symmetry breaking, has the Dirac operator
that is not of the product type. Using Wick rotation we derive explicitly the
Lagrangian of the model from the spectral action for a flat metric,
demonstrating the appearance of the topological $\theta$-terms for the
electroweak gauge fields.
