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Background: Since Google introduced Kotlin as an official programming language for developing Android apps in 2017, Kotlin has gained widespread adoption in Android development. The inter-operability of Java and Kotlin's design nature allows them to coexist and interact with each other smoothly within a project. Aims: However, there is limited research on how Java and Kotlin interact with each other in real-world projects and what challenges are faced during these interactions. The answers to these questions are key to understanding these kinds of cross-language software systems. Methods: In this paper, we implemented a tool named DependEx-tractor, which can extract 11 kinds of Kotlin-Java dependencies, and conducted an empirical study of 23 Kotlin-Java real-world projects with 3,227 Java and 8,630 Kotlin source files. Results: Our findings revealed that Java and Kotlin frequently interact with each other in these cross-language projects, with access and call dependency types being the most dominant. Compared to files interacting with other files in the same language, Java/Kotlin source files, which participate in the cross-language interactions, undergo more commits. Additionally, among all Kotlin-Java problematic interactions, we identified seven common mistakes, along with their fixing strategies. Conclusions: The findings of this study can help developers understand and address the challenges in Kotlin-Java projects.