Processes tend to interact with other processes and operate on various objects of different types. These objects can influence each other creating dependencies between sub-processes. Analyzing the conformance of such complex processes challenges traditional conformance-checking approaches because they assume a single-case identifier for a process. To create a single-case identifier one has to flatten complex processes. This leads to information loss when separating the processes that interact on some objects. This paper introduces an alignment approach that operates directly on these object-centric processes. We introduce alignments that can give behavior-based insights into how closely related the event data generated by a process and the behavior specified by an object-centric Petri net are. The contributions of this paper include a definition for object-centric alignments, an algorithm to compute them, a publicly available implementation, and a qualitative and quantitative evaluation. The qualitative evaluation shows that object-centric alignments can give better insights into object-centric processes because they correctly consider inter-object dependencies. Findings from the quantitative evaluation show that the run-time grows exponentially with the number of objects, the length of the process execution, and the cost of the alignment. The evaluation results motivate future research to improve the run-time and make object-centric alignments more applicable for larger processes.