  We investigate the quantum aspects of a charged hypermultiplet in deformed
N=(1,1) superspace with singlet non-anticommutative deformation of
supersymmetry. This model is a "star" modification of the hypermultiplet
interacting with a background Abelian vector superfield. We prove that this
model is renormalizable in the sense that the divergent part of the effective
action is proportional to the N=(1,0) non-anticommutative super Yang-Mills
action. We also calculate the finite part of the low-energy effective action
depending on the vector multiplet, which corresponds to the (anti)holomorphic
potential. The holomorphic piece is just deformed to the star-generalization of
the standard holomorphic potential, while the antiholomorphic piece is not. We
also reveal the component structure and find the deformation of the mass and
the central charge.
