Equivariant bundle
In geometry and topology, given a group G, an equivariant bundle is a fiber bundle such that the total space and the base space are both G-spaces and the projection map between them is equivariant: with some extra requirement depending on a typical fiber.
For example, an equivariant vector bundle is an equivariant bundle such that the action of G restricts to a linear isomorphism between fibres.