What is 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 spaces are both G-spaces and the projection map π {\displaystyle \pi } between them is equivariant: π ∘ g = g ∘ π {\displaystyle \pi \circ g=g\circ \pi } with some extra requirement depending on a typical fiber.

For example, an equivariant vector bundle is an equivariant bundle.