Assigning a (workflow)task to a Group from code can be tricky, but this trick works:
SPGroup group = SPWeb.UserGroups[“groupname”];
SPFieldUserValue groupvalue = new SPFIeldUserValue( group.ParentWeb, group.ID, group.Name);
SPWorkflowTaskProperties taskProperties = new SPWorkflowTaskProperties();
(Connect these taskproperties to the task to update)
taskProperties.AssignedTo = groupvalue.LookupValue;
To display these tasks in the task list the view 'Groups' has to be selected. they will not shop up in the 'My Tasks' view.