enable a manger programatically to view a certain user's worklist and operate on it -approval,rejection,delegation-

You can enable all managers to see the worklists of their direct reports and action their tasks in K2 Workspace if you enable that feature.  For this to work, your Active Directory must contain the reporting relationships.

Have a K2 administrator go into the K2 Workspace Management Console:

• 
  
• Drill down to Workflow Server
  
• Right-click and choose "Edit Settings..."
  
• Click the Advanced Settings tab
  
• About half way down the page is a checkbox that says "Display Worklist of Managed Users"
  
• Check the box and Save
  
• Do not modify any other settings unless you are aware of what they do

This is an all or nothing setting.  When turned on, it is turned on for everyone; when off, it is off for everyone. 

When that box is checked, all users who have direct reports in AD will be able to see their worklists of their reports in K2 Workspace.  The manager goes to K2 Workspace as usual.  On the home page that contains the task list, the manager should click on the Worklist panel in the lower left corner.  When that expands the manager will be able to drill down into the woklists of his/her reports.