Summary: The main objective of this paper is to analyze the \(p\)-local homotopy type of the complex projective Stiefel manifolds, and other analogous quotients of Stiefel manifolds. We take the cue from a result of Yamaguchi about the \(p\)-regularity of the complex Stiefel manifolds which lays down some hypotheses under which the Stiefel manifold is \(p\)-locally a product of odd dimensional spheres. We show that in many cases, the projective Stiefel manifolds are \(p\)-locally a product of a complex projective space and some odd dimensional spheres. As an application, we prove that in these cases, the \(p\)-regularity result of Yamaguchi is also \(S^1\)-equivariant.