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A G-solenoid is a laminated space whose leaves are copies of a single Lie group G and whose transversals are totally disconnected sets. It inherits a G-action and can be considered as a dynamical system. Free Z d -actions on the Cantor set as well as a large class of tiling spaces possess such a structure of G-solenoids. For a large class of Lie groups, we show that a G-solenoid can be seen as a projective limit of branched manifolds modeled on G. This allows us to give a topologicaldoi:10.1017/s0143385702001578 fatcat:na3fz3bq7nemtmun4fgfqplqeu