We analyze orbits of stars and dark matter out to three effective radii for 42 galaxies formed in cosmological zoom simulations .
Box orbits always dominate at the centers and z -tubes become important at larger radii .
We connect the orbital structure to the formation histories and specific features ( e.g .
disk , counter-rotating core , minor axis rotation ) in two-dimensional kinematic maps .
Globally , fast rotating galaxies with significant recent in situ star formation are dominated by z -tubes .
Slow rotators with recent mergers have significant box orbit and x -tube components .
Rotation , quantified by the \lambda _ { R } -parameter often originates from streaming motion of stars on z -tubes but sometimes from figure rotation .
The observed anti-correlation of h _ { 3 } and V _ { 0 } / \sigma in rotating galaxies can be connected to a dissipative formation history leading to high z -tube fractions .
For galaxies with recent mergers in situ formed stars , accreted stars and dark matter particles populate similar orbits .
Dark matter particles have isotropic velocity dispersions .
Accreted stars are typically radially biased ( \beta \approx 0.2 - 0.4 ) . In situ stars become tangentially biased ( as low as \beta \approx - 1.0 ) if dissipation was relevant during the late assembly of the galaxy .
We discuss the relevance of our analysis for integral field surveys and for constraining galaxy formation models .