Geometric phases appear as holonomies in principal bundles over quantum state spaces. In this work, we consider the case when the principal bundle itself is a Lie group and the quantum space of states a homogeneous space of that group. This structure allows the application of the theory of nonlinear realizations of symmetry for the construction non-Abelian geometric phases corresponding to this bundle structure. When the quantum state space is the complex Grassmann manifold U(N)/(U(N-k) × U(k)), we identify the total non-Abelian Aharonov-Anandan phase as the U(k)-valued cocycle of the U(N) action on the Grassmann manifold . We describe generalizations of this result in two cases: 1) the case of isospectral dynamics of mixed states, 2) the case of non-self adjoint dynamics over the Grassmannian.