So, you want the character to be able to hold this...?
EASY, just make the character look like hes hugging something, then make the map big enough to hold between his hands!!!, and you know how the portal gun uses the light button to change to the gravity gun??? well, you could do that with the map, so you could use the light button to roll it up, then unroll, then roll, then unroll!!! <gasping for air>