Tecla de atalho para JPopupMenu

import java.awt.Container;
import java.awt.FlowLayout;
import java.awt.event.ActionEvent;
import java.awt.event.KeyAdapter;
import java.awt.event.KeyEvent;

import javax.swing.AbstractAction;
import javax.swing.Action;
import javax.swing.JButton;
import javax.swing.JFrame;
import javax.swing.JMenuItem;
import javax.swing.JOptionPane;
import javax.swing.JPopupMenu;
import javax.swing.JTextField;
import javax.swing.KeyStroke;

public class Teste extends JFrame {
	
	JPopupMenu popupMenu;
	JButton okButton;
	
	public Teste() {
		Action okAction = new MessageAction("OK", "Ação OK");
		Action helpAction = new MessageAction("F1", "Ação Ajuda");

		okButton = new JButton(okAction);

		Container c = getContentPane();
		c.setLayout(new FlowLayout());
		c.add(new JTextField(40));
		c.add(okButton);
		
		getRootPane().setDefaultButton(okButton);
		
		getRootPane().getActionMap().put("F1", helpAction);
		getRootPane().getInputMap().put(KeyStroke.getKeyStroke(KeyEvent.VK_F1, 0), "F1");


		setSize(640, 480);
		setDefaultCloseOperation(EXIT_ON_CLOSE);
	}

	class MessageAction extends AbstractAction {
		String _msg;
		String nomeEvento;

		MessageAction(String name, String msg) {
			putValue(NAME, name);
			_msg = msg;
			nomeEvento = name;			
		}

		public void actionPerformed(ActionEvent evt) {			
			System.out.println(nomeEvento);
			if(nomeEvento.equals("F1")){				
				abrirPopup();
			}
		}
		
		private void abrirPopup(){  
			popupMenu = new JPopupMenu();
		
			JMenuItem file = new JMenuItem("File");
			JMenuItem edit = new JMenuItem("Edit");
			JMenuItem help = new JMenuItem("help");
			
			popupMenu.add(file);
			popupMenu.add(edit);
			popupMenu.add(help);
						
			popupMenu.show(okButton, 0, 10);  			
		}
		
		private void fecharPopup(){
			popupMenu.setVisible(false);
		}
	}
	
	
	
	public static void main(String[] args) {
		Teste t = new Teste();
		
		t.setVisible(true);
	}
}