  Description of periodically and resonantly driven quantum systems can lead to
solid state models where condensed matter phenomena can be investigated in time
lattices formed by periodically evolving Wannier-like states. Here, we show
that inseparable two-dimensional time lattices with the M\"obius strip geometry
can be realized for ultra-cold atoms bouncing between two periodically
oscillating mirrors. Effective interactions between atoms loaded to a lattice
can be long-ranged and can be controlled experimentally. As a specific example
we show how to realize a Lieb lattice model with a flat band and how to control
long-range hopping of pairs of atoms in the model.
