The rapid development of generative artificial intelligence (GenAI), including large language models (LLM), has merged to support students in their academic writing process. Keeping pace with the technical and educational landscape requires careful consideration of the opportunities and challenges that GenAI-assisted systems create within education. This serves as a useful and necessary starting point for fully leveraging its potential for learning and teaching. Hence, it is crucial to gather insights from diverse perspectives and use cases from actual users, particularly the unique voices and needs of student-users. Therefore, this study explored and examined students' perceptions and experiences about GenAI-assisted academic writing by conducting in-depth interviews with 20 Chinese students in higher education after completing academic writing tasks using a ChatGPT4-embedded writing system developed by the research team. The study found that students expected AI to serve multiple roles, including multi-tasking writing assistant, virtual tutor, and digital peer to support multifaceted writing processes and performance. Students perceived that GenAI-assisted writing could benefit them in three areas including the writing process, performance, and their affective domain. Meanwhile, they also identified AI-related, student-related, and task-related challenges that were experienced during the GenAI-assisted writing activity. These findings contribute to a more nuanced understanding of GenAI's impact on academic writing that is inclusive of student perspectives, offering implications for educational AI design and instructional design.