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We describe the structure of diffeological bundle of non formal classicalpseudo-differential operators over formal ones, and its structure group. Forthis, we give few results on diffeological principal bundles with (a priori) nolocal trivialization, use the smoothing connections alrealy exhibited by theauthor in previous works, and finish with open questions.

On diffeological principal bundles of non-formal pseudo-differential operators over formal ones