Innovation search is increasingly being performed as a collaborative effort between Artificial Intelligence (AI) agents and humans. To coordinate the activities related to the innovation search process, humans and AI engage in delegative interactions, where tasks are assigned or transferred between the two based on their respective strengths. While the concept of AI agency has begun to emerge in the literature, it remains largely conceptual. Our research contributes to this growing body of work by examining AI agency within the innovation search, offering empirical insights into how AI's autonomy influences human-AI collaboration. Through our study, we uncover that human-AI interaction is mediated by a complex delegation process, where tasks are dynamically delegated. Our study examines how the unique knowledge sets of both agents interact to shape problem definition, question formulation, and search processes. This interaction is demonstrated through three delegation styles: sequential, parallel, and iterative, each with its underlying rationale.