We compute the ring structure of wrapped Floer homology of a cotangent fiber in the A_k-type plumbing of cotangent bundle of spheres. Such a cotangent fiber can be seen as the fixed locus of some anti-symplectic involution. The main ingredient of the computation is an open string analogue of Seidel representation. We first apply the idea to compute the ring structure of V-shaped wrapped Floer homology. The usual wrapped Floer homology and the V-shaped wrapped Floer homology are known to be related by Viterbo transfer map. We determine the ring structure of wrapped Floer homology from that of V-shaped wrapped Floer homology using the Viterbo transfer map. This is a joint work with Myeonggi Kwon.