The simplest way is to use the Graphics View Framework. It provides mechanism for item selection, display of a rubber band rectangle, detection of intersection of the rubber band with the items, etc. Below is a self contained example. It lets you select and drag multiple items using either Ctrl/Cmd-click to toggle selection, or rubber banding.
OpenGL is used to render the background, and you can put arbitrary OpenGL content there.

main.cpp
#include <QApplication>
#include <QGraphicsView>
#include <QGraphicsScene>
#include <QGraphicsRectItem>
#include <QGLWidget>
static qreal rnd(qreal max) { return (qrand() / static_cast<qreal>(RAND_MAX)) * max; }
class View : public QGraphicsView {
public:
View(QGraphicsScene *scene, QWidget *parent = 0) : QGraphicsView(scene, parent) {
setViewport(new QGLWidget(QGLFormat(QGL::SampleBuffers)));
setViewportUpdateMode(QGraphicsView::FullViewportUpdate);
}
void drawBackground(QPainter *, const QRectF &) {
QColor bg(Qt::blue);
glClearColor(bg.redF(), bg.greenF(), bg.blueF(), 1.0f);
glClear(GL_COLOR_BUFFER_BIT | GL_DEPTH_BUFFER_BIT);
}
};
void setupScene(QGraphicsScene &s)
{
for (int i = 0; i < 10; i++) {
qreal x = rnd(1), y = rnd(1);
QAbstractGraphicsShapeItem * item = new QGraphicsRectItem(x, y, rnd(1-x), rnd(1-y));
item->setFlags(QGraphicsItem::ItemIsSelectable | QGraphicsItem::ItemIsMovable);
item->setPen(QPen(Qt::red, 0));
item->setBrush(Qt::lightGray);
s.addItem(item);
}
}
int main(int argc, char *argv[])
{
QApplication a(argc, argv);
QGraphicsScene s;
setupScene(s);
View v(&s);
v.fitInView(0, 0, 1, 1);
v.show();
v.setDragMode(QGraphicsView::RubberBandDrag);
v.setRenderHint(QPainter::Antialiasing);
return a.exec();
}