We here present rudiments of an approach to geometric actions in
noncommutative algebraic geometry, based on geometrically admissible actions of
monoidal categories. This generalizes the usual (co)module algebras over Hopf
algebras which provide affine examples. We introduce a compatibility of
monoidal actions and localizations which is a distributive law. There are
satisfactory notions of equivariant objects, noncommutative fiber bundles and
quotients in this setup.