Geometrical structure of the base and twisting of the graded fibre bundles used in modeling gravitation and elementary particles

To deseribe the unification of the fundamental interactions of elementary particles and gravitation the graded bundle mathematical structure $\zeta$ is needed. Its base $B$ is the 9-dimensional graded space having one scalar, four spinor and four vector dimensions. One-parametric family of the Poincaré group $1P$ is found. It is shown that any group of this family acts on its invariant subgroup and on the base $B$ in different ways. This situation is different from the classical one and point out at the nontriviality of the $\zeta$-bundle geometrical properties. The problem of twisting is discussed.