How to I display a sort arrow in the header of a list view column using C#?

You can use the following extension method to set the sort arrow to a particular column:

[EditorBrowsable(EditorBrowsableState.Never)]
public static class ListViewExtensions
{
    [StructLayout(LayoutKind.Sequential)]
    public struct HDITEM
    {
        public Mask mask;
        public int cxy;
        [MarshalAs(UnmanagedType.LPTStr)] public string pszText;
        public IntPtr hbm;
        public int cchTextMax;
        public Format fmt;
        public IntPtr lParam;
        // _WIN32_IE >= 0x0300 
        public int iImage;
        public int iOrder;
        // _WIN32_IE >= 0x0500
        public uint type;
        public IntPtr pvFilter;
        // _WIN32_WINNT >= 0x0600
        public uint state;

        [Flags]
        public enum Mask
        {
            Format = 0x4,       // HDI_FORMAT
        };

        [Flags]
        public enum Format
        {
            SortDown = 0x200,   // HDF_SORTDOWN
            SortUp = 0x400,     // HDF_SORTUP
        };
    };

    public const int LVM_FIRST = 0x1000;
    public const int LVM_GETHEADER = LVM_FIRST + 31;

    public const int HDM_FIRST = 0x1200;
    public const int HDM_GETITEM = HDM_FIRST + 11;
    public const int HDM_SETITEM = HDM_FIRST + 12;

    [DllImport("user32.dll", CharSet = CharSet.Auto, SetLastError = true)]
    public static extern IntPtr SendMessage(IntPtr hWnd, UInt32 msg, IntPtr wParam, IntPtr lParam);

    [DllImport("user32.dll", CharSet = CharSet.Auto, SetLastError = true)]
    public static extern IntPtr SendMessage(IntPtr hWnd, UInt32 msg, IntPtr wParam, ref HDITEM lParam);

    public static void SetSortIcon(this ListView listViewControl, int columnIndex, SortOrder order)
    {
        IntPtr columnHeader = SendMessage(listViewControl.Handle, LVM_GETHEADER, IntPtr.Zero, IntPtr.Zero);
        for (int columnNumber = 0; columnNumber <= listViewControl.Columns.Count - 1; columnNumber++)
        {
            var columnPtr = new IntPtr(columnNumber);
            var item = new HDITEM
                {
                    mask = HDITEM.Mask.Format
                };

            if (SendMessage(columnHeader, HDM_GETITEM, columnPtr, ref item) == IntPtr.Zero)
            {
                throw new Win32Exception();
            }

            if (order != SortOrder.None && columnNumber == columnIndex)
            {
                switch (order)
                {
                    case SortOrder.Ascending:
                        item.fmt &= ~HDITEM.Format.SortDown;
                        item.fmt |= HDITEM.Format.SortUp;
                        break;
                    case SortOrder.Descending:
                        item.fmt &= ~HDITEM.Format.SortUp;
                        item.fmt |= HDITEM.Format.SortDown;
                        break;
                }
            }
            else
            {
                item.fmt &= ~HDITEM.Format.SortDown & ~HDITEM.Format.SortUp;
            }

            if (SendMessage(columnHeader, HDM_SETITEM, columnPtr, ref item) == IntPtr.Zero)
            {
                throw new Win32Exception();
            }
        }
    }
}

Then, you can call the extension method like such:

myListView.SetSortIcon(0, SortOrder.Ascending);

It works by using P/Invoke to:

• Get the handle to the header control for a list view using the LVM_GETHEADER message.
• Get the information about a header column using the HDM_GETITEM message.
• It then modifies the fmt to set / clear the HDF_SORTDOWN and HDF_SORTUP flags on the returned HDITEM structure.
• Finally it re-sets the information usintg the HDM_SETITEM message.

This is what it looks like:

instead of messing with the Windows API, you can compromise and use characters that look like arrows (i picked them using charmap)

private void SetSortArrow(ColumnHeader head, SortOrder order)
{
    const string ascArrow = " ▲";
    const string descArrow = " ▼";

    // remove arrow
    if(head.Text.EndsWith(ascArrow) || head.Text.EndsWith(descArrow))
        head.Text = head.Text.Substring(0, head.Text.Length-2);

    // add arrow
    switch (order)
    {
        case SortOrder.Ascending: head.Text += ascArrow; break;
        case  SortOrder.Descending: head.Text += descArrow; break;
    }
}

SetSortArrow(listView1.Columns[0], SortOrder.None);       // remove arrow from first column if present
SetSortArrow(listView1.Columns[1], SortOrder.Ascending);  // set second column arrow to ascending
SetSortArrow(listView1.Columns[1], SortOrder.Descending); // set second column arrow to descending