Welcome aboard, taibhse. Tá fáilte romhat!
I'd say that 'gníomhaíochta' or 'gníomhaireachta' is probably what was intended. It seems to me (in English and in Irish) to be more like a heading for a newspaper piece or internet story than an actual sentence. There is obviously a 'tá' missing at the start if making a sentence was the intention.
I don't know if this will satisfy patrickj though!
I take his point to an extent. My motto when translating is to try to translate the meaning rather than the words. Also, don't complicate things when there is a simple solution. So, what exactly is an 'action group', can anyone tell me? To make a sentence I'd be inclined to just write:
Tá grúpa ag iarraidh ar Fhoras na Gaeilge athmhachnamh a dhéanamh ar chinneadh an Bhoird
or leave out the 'tá' if it is to be used 'headline' style.
I don't see anything wrong with that if somebody in the Gaeltacht or outside it wants to describe what is happening. Board meetings and decisions, rethinks etc are part of modern life within the Gaeltacht and outside it. While the language of An tOileánach is beautiful and we have a lot to learn from it, I think we can't confine the language to that either if it is to remain a viable, living relevant language. There must be room for both and we can only do our best to ensure that when new words and terms are needed in Irish that they keep the idiom and structure of the language as much as possible. That's my opinion anyway.
I suppose an action group are a group that wish to project themselves as not just being a 'talking shop'? Perhaps posters can suggest adjectives (keep it clean please

) to follow 'grúpa' in that case.
I think your question, taibhse, was more grammatical than anything else and thus, to finish on that point,
Gníomhaíochta is the genitive singular of gníomhaíocht
Gníomhaireachta is the genitive singular of gníomhaireacht
Their meanings are basically the same, covering 'activity' or 'performance' or 'agency'. I'm not sure that they (or action in English) bring very much to the table in this case. Maybe they are a community group which would translate as 'grúpa pobail'.
Now that you've started to post, taibhse, lean ort agus fáilte!