Hope I am not misunderstanding your needs here but...
Providing your cell is a DataGridViewCheckBoxCell you can do the following things...
To Set:
dataGridView.Rows[0].Cells[0].Value = true;
To Read:
bool checked = (bool)dataGridView.Rows[0].Cells[0].Value;
To Evaluate:
if((bool)dataGridView.Rows[0].Cells[0].Value)
NOTE: If you are reading a checkbox cells upon save you may want to add the following code to a CellMouseUp event on your DataGridView:
void DataGridViewCellMouseUp(object sender, DataGridViewCellMouseEventArgs e)
{
dataGridViewFiles.EndEdit();
}