Reaction of alkyl bromide in presence of piperidine
@User6376297 raised a question:


  "Could the cyclopropane ring behave like a double bond, making this the analogue of an allyl bromide, and yielding $\ce{R2NCH2CH2CH=CH-tBu}$ by attack on a cyclopropyl $\ce{CH2}$ and ring opening?" Especially given the steric hindrance near the carbon bearing the leaving group. 


Indeed, that is the process going on in this case when the reaction was taken place in piperidine either at refluxing conditions or at room temperature. When (1-bromo-2,2-dimethylpropyl)cyclopropane (the alkyl bromide in question) was reacted in refluxing piperidine, it has yielded $88\%$ of (E)-1-(5,5-dimethylhex-3-en-1-yl)piperidine as a major product, which corresponds to the homoallylic analogue of the well-known SN2 process observed with allylic halide. 

In addition, $8\%$ of 1-(1-cyclopropyl-2,2-dimethylpropyl)piperidine was also yielded as a minor product (Ref. 1 &amp; 2). The authors claimed the formation of the minor product was not compatible with simple SN2 displacement due to the great steric hindrance imposed by the neighboring $\ce{t-Bu}$ and cyclopropyl groups, but the tight ion-pair mechanism (not separated by solvent) may explain the presence of SN2 product very well.

The percent yields of SN2' and SN2 products for the reaction at $\pu{25^\circ C}$ had been $73\%$ and $8\%$, respectively.

References:


Reaction of amines with cyclopropylcarbinyl halides: SN2' or
solvolysis?: J. Org. Chem., 1985, 50(24), 4815–4821 (https://doi.org/10.1021/jo00224a033).
Homoallylic substitution reaction of piperidine with 1-bromo-1-cyclopropylalkanes: Tetrahedron Lett., 1983, 24(46), 5031–5034 (https://doi.org/10.1016/S0040-4039(00)94033-4).