Light Yagami manipulates public opinion to support Kira's actions by using the Death Note to kill criminals and create a sense of fear and awe in society. He portrays Kira as a righteous and just figure who is targeting only criminals, thus gaining public support for his actions. Additionally, Light strategically releases information to the media to shape the narrative in a way that portrays Kira in a positive light, further influencing public opinion in favor of Kira's actions.
