How to use the map for my group?

Hi, I just discovered OpenStreetMaps, and it’s a very nice initiative!

I would like to know is there is the possibility (like in Google “MyMaps”) to add (draw) zones above the map for my own purpose (eg quarters in town where one of my group members is active) . I want to share these polygons with them, so the can edit them , indicating if they can “work” on those areas (put leaflets in the mailboxes of some streets), and edit them again if they have finished the job.

If i’ts possible, I should of course prefer not to work with a “MuchProfit”-organisation like Google.

thank you

perhaps http://umap.openstreetmap.fr/ does what you want?

Or maybe a OSM task manager like http://learnosm.org/en/coordination/tasking-manager/ ???
Its free to use under a BSD license and can easily be installed on your own server.

There are also some installations available for personal use for OSM activities:
http://wiki.openstreetmap.org/wiki/OSM_Tasking_Manager#Operational_installations_of_the_Tasking_Manager