/usr/lib/gcc/avr/4.8.2/include/ is in gcc-avr 1:4.8-2.1.
This file is owned by root:root, with mode 0o755.
..
/usr/lib/gcc/avr/4.8.2/include-fixed/README
/usr/lib/gcc/avr/4.8.2/include-fixed/limits.h
/usr/lib/gcc/avr/4.8.2/include-fixed/syslimits.h
/usr/lib/gcc/avr/4.8.2/include/float.h
/usr/lib/gcc/avr/4.8.2/include/iso646.h
/usr/lib/gcc/avr/4.8.2/include/stdalign.h
/usr/lib/gcc/avr/4.8.2/include/stdarg.h
/usr/lib/gcc/avr/4.8.2/include/stdbool.h
/usr/lib/gcc/avr/4.8.2/include/stddef.h
/usr/lib/gcc/avr/4.8.2/include/stdfix-gcc.h
/usr/lib/gcc/avr/4.8.2/include/stdfix.h
/usr/lib/gcc/avr/4.8.2/include/stdint-gcc.h
/usr/lib/gcc/avr/4.8.2/include/stdint.h
/usr/lib/gcc/avr/4.8.2/include/stdnoreturn.h
/usr/lib/gcc/avr/4.8.2/include/unwind.h
/usr/lib/gcc/avr/4.8.2/include/varargs.h