  The Boltzmann equation framework for inelastic Maxwell models is considered
to determine the transport coefficients associated with the mass, momentum and
heat fluxes of a granular binary mixture in spatially inhomogeneous states
close to the simple shear flow. The Boltzmann equation is solved by means of a
Chapman-Enskog-like expansion around the (local) shear flow distributions
$f_r^{(0)}$ for each species that retain all the hydrodynamic orders in the
shear rate. Due to the anisotropy induced by the shear flow, tensorial
quantities are required to describe the transport processes instead of the
conventional scalar coefficients. These tensors are given in terms of the
solutions of a set of coupled equations, which can be analytically solved as
functions of the shear rate $a$, the coefficients of restitution $\alpha_{rs}$
and the parameters of the mixture (masses, diameters and composition). Since
the reference distribution functions $f_r^{(0)}$ apply for arbitrary values of
the shear rate and are not restricted to weak dissipation, the corresponding
generalized coefficients turn out to be nonlinear functions of both $a$ and
$\alpha_{rs}$. The dependence of the relevant elements of the three diffusion
tensors on both the shear rate and dissipation is illustrated in the tracer
limit case, the results showing that the deviation of the generalized transport
coefficients from their forms for vanishing shear rates is in general
significant. A comparison with the previous results obtained analytically for
inelastic hard spheres by using Grad's moment method is carried out showing a
good agreement over a wide range of values for the coefficients of restitution.
Finally, as an application of the theoretical expressions derived here for the
transport coefficients, thermal diffusion segregation of an intruder immersed
in a granular gas is also studied.
