A finite-strain phase-field model of coupled deformation twinning and crystal plasticity is developed in the paper. Twinning is treated as a displacive transformation characterized by a volume-preserving stretch rather than a simple shear, the latter considered in the conventional approach. It is shown that the two approaches are equivalent in the sharp-interface description, but not in the diffuse-interface description. In the proposed stretch-based kinematics, each pair of conjugate twinning systems is represented by a single twin deformation variant, and thus a single order parameter suffices to consistently describe the two conjugate twinning systems, thereby treating them equally. The model is formulated in the framework of incremental energy minimization, which, upon time discretization, leads to a quasi-optimization problem due to the specific form of the incremental potential within the diffuse interfaces. To facilitate finite-element implementation, a micromorphic formulation of the model is employed. As an application, tensile twinning in HCP magnesium alloys is examined, and a set of comprehensive 2D plane-strain problems is studied to illustrate the features of the proposed approach. [ABSTRACT FROM AUTHOR]