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For the q-deformation Gq, 0 < q < 1, of any simply connected simple compact Lie group G we construct an equivariant spectral triple which is an isospectral deformation of that defined by the Dirac operator D on G. Our quantum Dirac operator Dq is a unitary twist of D considered as an element of U g ⊗ Cl(g). The commutator of Dq with a regular function on Gq consists of two parts. One is a twist of a classical commutator and so is automatically bounded. The second is expressed in terms of thedoi:10.1515/crelle.2010.026 fatcat:qvikzfwohndnhnenpd5ztmyycu