Selectors on commands run by /execute are not run as if by /execute's target

When run directly by a player the following command works as expected.

Kills Creepers in a large area around the player: /kill @e[type=Creeper,x=-128,dx=256,z=-128,dz=256,y=0,dy=256]

Selectors on commands run by execute are not run as if by the target, but by whatever is running the execute command instead.
Kills Creepers in a large area around the executor (e.g. a command block) and not all players: execute @a ~ ~ ~ kill @e[type=Creeper,x=-128,dx=256,z=-128,dz=256,y=0,dy=256]