/usr/lib/gcc-cross/aarch64-linux-gnu/4.8/include/ is in libobjc-4.8-dev-arm64-cross 4.8.5-4ubuntu1cross2.
This file is owned by root:root, with mode 0o755.
..
/usr/lib/gcc-cross/aarch64-linux-gnu/4.8/include/objc/
/usr/lib/gcc-cross/aarch64-linux-gnu/4.8/include/objc/NXConstStr.h
/usr/lib/gcc-cross/aarch64-linux-gnu/4.8/include/objc/Object.h
/usr/lib/gcc-cross/aarch64-linux-gnu/4.8/include/objc/Protocol.h
/usr/lib/gcc-cross/aarch64-linux-gnu/4.8/include/objc/message.h
/usr/lib/gcc-cross/aarch64-linux-gnu/4.8/include/objc/objc-decls.h
/usr/lib/gcc-cross/aarch64-linux-gnu/4.8/include/objc/objc-exception.h
/usr/lib/gcc-cross/aarch64-linux-gnu/4.8/include/objc/objc-sync.h
/usr/lib/gcc-cross/aarch64-linux-gnu/4.8/include/objc/objc.h
/usr/lib/gcc-cross/aarch64-linux-gnu/4.8/include/objc/runtime.h
/usr/lib/gcc-cross/aarch64-linux-gnu/4.8/include/objc/thr.h