using WPF, c#, VS 2012
Try to implement some custom behaviors for UI with WPF.
Currently create class that inherited from Behavior<FrameworkElement>
Idea: create one area on UI for entering name (I used textBox) - another area (Rectangle) - press and see some action with data from prev field.
What was done:
Class for implementing idea (class with Behavior)
class SayHello: Behavior<FrameworkElement>
{
    public string Words { get; set; }
    protected override void OnAttached()
    {
        AssociatedObject.MouseLeftButtonUp += OnMouseClick;
    }
    private void OnMouseClick(object sender, 
                System.Windows.Input.MouseButtonEventArgs e)
    {
        MessageBox.Show(string.Format("hello , {0}", Words));
    }
    protected override void OnDetaching()
    {
        AssociatedObject.MouseLeftButtonUp -= OnMouseClick;
    }        
}
XAML:
<Window
    xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation"
    xmlns:x="http://schemas.microsoft.com/winfx/2006/xaml"
    xmlns:i="http://schemas.microsoft.com/expression/2010/interactivity"
    xmlns:ei="http://schemas.microsoft.com/expression/2010/interactions" 
    xmlns:local="clr-namespace:CH08.MovingCircle"
    x:Class="CH08.MovingCircle.MainWindow"
    Title="MainWindow" Height="350" Width="525">
<Canvas>
    <Border Canvas.Top="220" BorderBrush="Black" 
            BorderThickness="2">
        <TextBox x:Name="_enteredWords" Width="200"/>
    </Border>
    <Rectangle Stroke="Blue" Canvas.Top="250" Fill="Aquamarine"
               Width="200" Height="50">
        <i:Interaction.Behaviors>
            <local:SayHello 
                Words="{Binding Text, ElementName=_enteredWords}"/>
        </i:Interaction.Behaviors>
    </Rectangle>
</Canvas>
Got error : A 'Binding' cannot be set on the 'Words' property of type 'SayHello'. A 'Binding' can only be set on a DependencyProperty of a DependencyObject...
If i change part of XAML to
        <Rectangle Stroke="Blue" Canvas.Top="250" Fill="Aquamarine"
               Width="200" Height="50">
        <i:Interaction.Behaviors>
            <local:SayHello 
                Words="Adbracadabra"/>
        </i:Interaction.Behaviors>
    </Rectangle>
- all works (mean just remove binding).
Question: are it's possible to create binding to properties for class with custom behavior? If yes, how can i do this?
EDIT:
As was suggested by vfabre - changed property to dependency property
 public string Words
    {
        get { return (string)GetValue(WordsProperty); }
        set { SetValue(WordsProperty, value); }
    }
    // Using a DependencyProperty as the backing store for Words. 
    //This enables animation, styling, binding, etc...
    public static  DependencyProperty WordsProperty =
        DependencyProperty.Register("Words", typeof(string),
        typeof(SayHello), new PropertyMetadata(default(string)));
Result

 
    