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Let $(N,c_N)$ be a complex vector bundle equipped with a real structure overa real curve $(\Sigma,c_\Sigma)$ of genus $g \geq 0$. We compute the sign ofthe action of the automorphisms of $(N,c_N)$ lifting the identity of $\Sigma$on the orientations of the determinant line bundle over the space of realCauchy-Riemann operators on $(N,c_N)$. This sign can be obtained as the productof two terms. The first one computes the signature of the permutations inducedby the automorphisms acting on the $Pin^\pm$ structures of the real part of$(N,c_N)$. The second one comes from the action of the automorphisms of$(N,c_N)$ on the bordism classes of real Spin structures on$(\Sigma,c_\Sigma)$.

Automorphismes r\'eels d'un fibr\'e et op\'erateurs de Cauchy-Riemann