'sets' has already connotations and is used widely. 'tasklets' is fairly unique and is probably already commonly used within the working group.

'user_tasks' does have a sense of ownership about it which is helpful/clear, then again tasklet/s does have a good ring to it.

post critical suggestion... 'shreds', deriving from 'shared threads' truncated to 'shreads' perhaps, though the latter could indicate code of an undesired nature. The former, well I never put a cpu through a paper shredder but maybe fun to see what happens. And welcome to the shredding renaissance :p