Conventional thoughts of inertia are internal to an object, not satisfactory for a number of reasons.
Limiting speed of light is telling that a moving object interacts with the local space time, without which there would not be a limitation of speed for objects.
Bringing velocity terms into Polarizable Vacuum theory results in frame dragging, and removes the main objection to PV theory.
GR from equation 107 in Princeton lectures of 1921 gives decreasing of light speed during gravitational acceleration. With Equivalence the Lagrangian requires kinetic acceleration to increase local light speed measured by a traveler within limitations, and not significant at low speeds..
With locally variable speed of light for high speed, conventional equations of energy and momentum make an incomplete set, requiring Partition Theory and Hierarchy of Planck h to complete the set.
Bringing Planck h into equations expresses quantum exchange of energy between a moving object and its local stress field. It requires a zero velocity reference.
GR allows any speed to be chosen as a zero velocity reference, isotropic CMB sometimes being convenient as a zero reference anywhere.
Inertia in a local stress curvature field inside and around an object seems to agree with other information. A curl free inertial vector field is implied.
Is Inertia Expressed In Stress Curvature Like Frame Dragging?