This old male decides to lay down
afternoon stakes. (Afternoon nap?) He's digging a hollow to rest
his giant hips

I've never heard this expression. What's the context?

I think that to "lay down stakes" (or maybe "put down stakes") means to claim a territory. "Stake a claim" would be a similar, but more common expression.
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They're showing a kangaroo that rests from the killing sun.
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