In this study, we investigate the best remanufacturing strategy for the original equipment manufacturer (OEM) and independent remanufacturer (IR) in an innovative industry where the consumer valuation of the products increases with the level of innovation, and we characterize how the best strategy changes with the identity of the remanufacturer. Our work differs from existing articles that investigate the remanufacturing strategy in the presence of quality decisions, by actively including the innovative features in the remanufactured products, as opposed to passively carrying over product quality to the remanufactured products. We consider three remanufacturing strategies: (i) not remanufacturing, (ii) remanufacturing without adding innovative features, and (iii) remanufacturing adding innovative features (upgrading). To analyze the problem, we create a single-period model where the OEM determines the level of innovation and the quantity of new products, in both competitive settings, and either the OEM or IR determines the remanufacturing quantity depending on the competitive setting. We investigate how the firms' environmental impact and the consumer surplus are affected by the competition and the remanufacturing strategy.