We find Fredholm criteria and a formula for the index of an arbitrary operator in the Banach algebra of singular integral operators
with piecewise continuous coefficients on Nakano spaces (generalized Lebesgue spaces with variable exponent) with Khvedelidze weights over either Lyapunov curves or Radon curves without cusps.
These results ``localize'' the Gohberg-Krupnik Fredholm theory with respect to the variable exponent.Fundação para a Ciência e a Tecnologia (FCT
