The Collective Perception (CP) service has brought significant enhancements to the awareness of Connected and Autonomous Vehicles (CAVs) by enabling the sharing of perception information and mitigating field-of-view-related problems. Despite this, security risks remain critical, and even legitimate vehicles may carry out falsification attacks by sending false perception information, which can result in severe accidents. In this work, we specifically focus on this type of attack by introducing the fake objects attack, where the attacker sends non-existent objects in its CPMs. We propose a detection mechanism based on two codependent components: the verification and tagging process and the trust calculation process. The first component enables checking the existence of objects with trusted surroundings based on their trust scores, which are calculated by the second process. Three attack scenarios are used to demonstrate significant accuracy in detecting fake objects through the evaluation of false positive and false negative rates, as well as identifying the attacker vehicle by evaluating the trust scores of all present vehicles.