  The purpose of this paper is to investigate an algebraic version of the
double complex transfer, in particular the classes in the two-line of the
Adams-Novikov spectral sequence which are the image of comodule primitives of
the MU-homology of the product of two copies of infinite complex projective
space via the algebraic double transfer. These classes are analysed by two
related approaches; the first, p-locally for an odd prime, by using the
morphism induced in MU-homology by the chromatic factorization of the double
transfer map together with the f'-invariant of Behrens (for p>=5). The second
approach uses the algebraic double transfer and the f-invariant of Laures.
