Crystal lattice rotations induced by twinning and shear banding developed in a Cu–8 at.% Al alloy (representative of fcc metals with low stacking fault energy) have been examined in order to investigate the influence of bands on slip propagation across a structure of twin-matrix layers and the resulting texture evolution. The microstructure and texture of oriented single crystal plane strain compressed up to 80% 77 K were characterized by transmission electron microscopy (TEM) including TEM orientation mapping. It is shown that the strong, initial texture changes are due to deformation twinning. Two families of deformation twins, symmetric with respect to the plane perpendicular to the extension direction, are observed. However, only one of them plays a dominant role in strain accommodation. At larger deformations, twin-matrix deflection within some narrow areas leads to kink-type bands, and this is crucial for understanding further texture transformations. The kink bands are precursors of shear bands (SB). It is shown by detailed TEM orientation mapping how the structure of twins and matrix is incorporated into a SB, and what kind of the dislocation mechanisms are responsible for strain accommodation at the macro-scale. It was found that the re-orientation of the main (1 1 1) twinning planes towards the SB plane facilitates further dislocation slip in the shear direction. Finally, a crystallographic description of SB formation in completely twinned fcc metals is proposed based on lattice re-orientations due to localized kinking.