We use JIRA Workflow Toolbox, specifically the "Set a field as a function of other fields" postfunction, to do something similar to what I think you're describing.
You specify the source field (say Region, where values the customer selects are North, South, East, West), and the target field (Assignee), and then you set how the values from the first should write to the second.
As Nic said, you can't assign groups to the assignee field, but if you had a group user custom field, you could use this to set that field too.
...be more productive while being fun to use at the same time. For some, getting started can be a bit intimidating. This is especially true if Jira Service Desk is your first exposure to Atlassian...
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