Creating tasks on cases - task to someone other than owner

Creating tasks on cases - task to someone other than owner

Hi there - I'm just trying to work out how cases work and how the work on them might be assigned out...... here is our scenario

Person A enters a case - a client who has complained about a product.
Person A wants to assign the resolution of the case to person B

When I create a task on a case it seems to be automatically assigned to the case owner (i.e. the person who input it) and this doesn't seem to be changable.  Is this correct?  Is there a way to link a case to a task and assign it to someone else?

Cheers Fiona