Using the asymptotic transport theory and the reactor image method in a reactor lattice, the group theory is applied to develop a solid-state physics formalism, generalizing Nelkin’s theory for homogeneous media. The eigenvalues of the transport operator are shown to be classified according to the representations of the lattice symmetry group, while the corresponding flux eigenfunctions form a basis for those representations. These flux eigenfunctions have a Bloch form that can be interpreted as a factorization of the flux into a macroscopic and a microscopic shape. Finally, the transport eigenvalue problem is shown to be reduced to a unit cell eigenvalue problem for a modified transport equation, the resolution of which can be simplified by symmetry considerations in the choice of trial functions for some variational principle.