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Basic Forms and Orbit Spaces: a Diffeological Approach
Symmetry, integrability and geometry: methods and applications, Tome 12 (2016) Cet article a éte moissonné depuis la source Math-Net.Ru

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If a Lie group acts on a manifold freely and properly, pulling back by the quotient map gives an isomorphism between the differential forms on the quotient manifold and the basic differential forms upstairs. We show that this result remains true for actions that are not necessarily free nor proper, as long as the identity component acts properly, where on the quotient space we take differential forms in the diffeological sense.
Keywords: diffeology; Lie group actions; orbit space; basic differential forms. 
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Yael Karshon; Jordan Watts. Basic Forms and Orbit Spaces: a Diffeological Approach. Symmetry, integrability and geometry: methods and applications, Tome 12 (2016). http://geodesic.mathdoc.fr/item/SIGMA_2016_12_a25/

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