  Grayson, developing ideas of Quillen, has made computations of the K-theory
of "semi-linear endomorphisms". In the present text we develop a technique to
compute these groups in the case of Frobenius semi-linear actions. The main
idea is to interpret the semi-linear modules as crystals and use a positive
characteristic version of the Riemann-Hilbert correspondence. We also compute
the K-theory of the category of etale constructible p-torsion sheaves.
