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How to keep data stored in generic List<T> available during all processes at the same page.

I need to Save selected items in generic List<T> . and keep it until selecting all items needed. Then by pressing the second button "show search results" .
My problem was when I press the second pagination page number, I lose the selected items in previous page "the List<T> is reset".
Could anyone help me please to keep these selected items accumulated to the List<T> until I finish all items I need to select from all available pages.

<%@ Page Language="C#" AutoEventWireup="true" CodeBehind="myForm_EE.aspx.cs" Inherits="myGoogleLike_webapp.myForm_EE" %>

<!DOCTYPE html>

<html xmlns="http://www.w3.org/1999/xhtml">
<head runat="server">
    <title></title>
</head>
<body>
    <form id="form1" runat="server">
    <div>
        <asp:Label ID="lblHead" runat="server" Text=" Enter Your searching test here"></asp:Label>
        <br />
        <asp:TextBox ID="mySearch_TextBox" runat="server"></asp:TextBox>
        <asp:Button ID="search_Button" runat="server" Text="Go" OnClick="search_Button_Click" />
        <br />

        <asp:GridView ID="GridView1" runat="server"  AllowPaging="True" OnPageIndexChanging="GridView1_PageIndexChanging" PageSize="20" AutoGenerateColumns="False" >
            <Columns>
                <asp:TemplateField>
                    <ItemTemplate>
                        <asp:CheckBox ID="CheckBox1" runat="server" AutoPostBack="True"  />
                    </ItemTemplate>
                </asp:TemplateField>
                <asp:TemplateField HeaderText="Employee ID">
                    <ItemTemplate>
                        <asp:Label ID="lblProductID" runat="server" Text='<%# Bind("ProductID") %>'></asp:Label>
                    </ItemTemplate>
                </asp:TemplateField>
                <asp:BoundField DataField="Name" HeaderText="Name" />
                <asp:BoundField DataField="Price" HeaderText="Price" />
            </Columns>
        </asp:GridView>
        <br />
        <asp:Button ID="Button1" runat="server" Text="show search results"  />
    </div>
    </form>
</body>
</html>

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using System;
using System.Collections.Generic;
using System.Linq;
using System.Web;
using System.Web.UI;
using System.Web.UI.WebControls;

namespace myGoogleLike_webapp
{
    public partial class myForm_EE : System.Web.UI.Page
    {
        salesDataContext db = new salesDataContext();
        protected void Page_Load(object sender, EventArgs e)
        {

        }

        protected void search_Button_Click(object sender, EventArgs e)
        {
            BindData();
        }

        protected void GridView1_PageIndexChanging(object sender, GridViewPageEventArgs e)
        {
            GridView1.PageIndex = e.NewPageIndex;
            BindData();
        }
        private void BindData()
        {
            string myString = mySearch_TextBox.Text.Trim();
            
            var myProducts = (from mySection in db.Products
                              where mySection.Name.Contains(myString) 
                              select mySection).ToList();

            if ((myProducts != null) && (myProducts.Count() > 0))
            {
                GridView1.DataSource = myProducts;
                GridView1.DataBind();
            }
        }
    }
}

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