In this paper, the authors develop the theory of \({\cal{S}}_{T}\) -graded modules to study some kinds of graded structures on reducing subspaces. They introduce some concepts and find an effective way to study \({\cal{S}}_{T}\) -graded modules, which they name the kernel method. For its application, they define standard models for some multiplication operators and special Toeplitz operators, and show that these standard models can be solved by the kernel method. The authors also generalize the kernel method to arbitrary Hilbert spaces without any \({\cal{S}}_{T}\) -graded condition. Finally, for any bounded operator T, they can find a reducing subspace that is \({\cal{S}}_{T}\) -graded.
