/usr/lib/gcc-cross/ is in libobjc-8-dev-i386-cross 8-20180414-1ubuntu2cross1.
This file is owned by root:root, with mode 0o755.
..
/usr/lib/gcc-cross/i686-linux-gnu/
/usr/lib/gcc-cross/i686-linux-gnu/8/
/usr/lib/gcc-cross/i686-linux-gnu/8/include/
/usr/lib/gcc-cross/i686-linux-gnu/8/include/objc/
/usr/lib/gcc-cross/i686-linux-gnu/8/include/objc/NXConstStr.h
/usr/lib/gcc-cross/i686-linux-gnu/8/include/objc/Object.h
/usr/lib/gcc-cross/i686-linux-gnu/8/include/objc/Protocol.h
/usr/lib/gcc-cross/i686-linux-gnu/8/include/objc/message.h
/usr/lib/gcc-cross/i686-linux-gnu/8/include/objc/objc-decls.h
/usr/lib/gcc-cross/i686-linux-gnu/8/include/objc/objc-exception.h
/usr/lib/gcc-cross/i686-linux-gnu/8/include/objc/objc-sync.h
/usr/lib/gcc-cross/i686-linux-gnu/8/include/objc/objc.h
/usr/lib/gcc-cross/i686-linux-gnu/8/include/objc/runtime.h
/usr/lib/gcc-cross/i686-linux-gnu/8/include/objc/thr.h
/usr/lib/gcc-cross/i686-linux-gnu/8/libobjc.a
/usr/lib/gcc-cross/i686-linux-gnu/8/libobjc.so