Abstract：The classification symmetry protected topological (SPT) phases with on-site symmetry in the interacting fermionic systems with arbitrary dimensions are well established by a generalized group super-cohomology theory, but the space group counterpart's classification is still in a puzzle. In this talk, I will introduce the classification of interacting fermionic SPT phases with wallpaper group symmetries in (2+1)-dimensional system. Furthermore, with the obtained classification data, we discuss the recently proposed correspondence principle between crystalline topological phases and those with internal symmetries through the explicit lower-dimensional block-state decoration.