We propose a domain-decomposition method to simulate articulated deformable characters entirely within a subspace framework. The method supports quasistatic and dynamic deformations, nonlinear kinematics and materials, and can achieve interactive time-stepping rates. To avoid artificial rigidity, or ``locking,'' associated with coupling low-rank domain models together with hard constraints, we employ penalty-based coupling forces. The multi-domain subspace integrator can simulate deformations efficiently, and exploits efficient subspace-only evaluation of constraint forces between rotated domains using a novel Fast Sandwich Transform (FST). Examples are presented for articulated characters with quasistatic and dynamic deformations, and interactive performance with hundreds of fully coupled modes. Using our method, we have observed speedups of between three and four orders of magnitude over full-rank, unreduced simulations.