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Let X = X ¯ − D be a smooth quasi-projective curve. We previously constructed a Deligne–Hitchin moduli space with Hecke gauge groupoid for connections of rank 2. We extend this construction to the case of any rank r , although still keeping a genericity hypothesis. The formal neighborhood of a preferred section corresponding to a tame harmonic bundle is governed by a mixed twistor structure. [ABSTRACT FROM AUTHOR]