Группировка и сортировка привязанных изменяющихся данных

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Windows;
using System.Windows.Controls;
using System.Windows.Data;
using System.Windows.Documents;
using System.Windows.Input;
using System.Windows.Media;
using System.Windows.Media.Imaging;
using System.Windows.Navigation;
using System.Windows.Shapes;
using System.Collections.ObjectModel;
using System.ComponentModel;
 
namespace Practice
{
  /// <summary>
  /// Interaction logic for Window1.xaml
  /// </summary>
  /// 
  public partial class Window1:Window
  {
    TestCollection list;
    TestClass[] a= new TestClass[]{ new TestClass("Иванов И.И.","somewhere1",true),
        new TestClass("Petrov P.P.","somewhere2"),
        new TestClass("Sidorov S.S.","somewhere3"),
        new TestClass("Smirnova L.D.","somewhere4")};
    private static int index=0;
 
    public Window1()
    {
      InitializeComponent();
      list=new TestCollection();
      list.Add(a[0]);
      myListBox.ItemsSource=list.List;
    }
 
    private void Button_Click(object sender,RoutedEventArgs e)
    {
      if (index<(a.Length-1))
      {
        list.Add(a[++index]);
      }
    }
 
    private void Button_Click_1(object sender,RoutedEventArgs e)
    {
      list.FixPerson(index);
    }
  }
 
  public class TestClass:INotifyPropertyChanged
  {
    public TestClass(string fio,string adress):this(fio,adress,false)
    {
    }
 
    public TestClass(string fio,string adress,bool fix)
    {
      this.fio=fio;
      this.adress=adress;
      this.fix=fix;
    }
 
    //INotifyPropertyChanged Members
    public event PropertyChangedEventHandler PropertyChanged;
    private void raisePropertyChanged(string propertyName)
    {
      if (PropertyChanged!=null)
        PropertyChanged(this,new PropertyChangedEventArgs(propertyName));
    }
 
    private bool fix=false;
    public bool Fix
    {
      get { return fix; }
      set
      {
        fix=value;
        raisePropertyChanged("Fix");
        raisePropertyChanged("FIO");
      }
    }
 
    private string fio;
    public string FIO
    {
      get
      {
        if (fix)
          return "(fixed) "+fio;
        else
          return fio;
      }
    }
 
    private string adress;
    public string Adress { get { return adress; } }
  }
 
  public class TestCollection
  {
    private ObservableCollection<TestClass> list=new ObservableCollection<TestClass>();
    public ObservableCollection<TestClass> List
    {
      get { return list; }
    }
 
    public TestCollection()
    {
      ICollectionView view=CollectionViewSource.GetDefaultView(list);
      view.SortDescriptions.Add(new SortDescription("FIO",ListSortDirection.Ascending));
      view.GroupDescriptions.Add(new PropertyGroupDescription("Fix",new FixGrouper()));
    }
 
    public class FixGrouper:IValueConverter
    {
      public object Convert(object value,Type targetType,object parameter,System.Globalization.CultureInfo culture)
      {
        if ((bool)value)
          return "Clicked";
        else
          return "Not Clicked";
      }
 
      public object ConvertBack(object value,Type targetType,object parameter,System.Globalization.CultureInfo culture)
      {
        throw new NotImplementedException();
      }
    }
 
    public void Add(TestClass person)
    {
      list.Add(person);
    }
 
    public void FixPerson(int index)
    {
      list[index].Fix=true;
    }
  }
}